photoelectric effect experiment name

Photoelectric Effect

Under the right circumstances light can be used to push electrons, freeing them from the surface of a solid. This process is called the photoelectric effect (or photoelectric emission or photoemission ), a material that can exhibit this phenomenon is said to be photoemissive , and the ejected electrons are called photoelectrons ; but there is nothing that would distinguish them from other electrons. All electrons are identical to one another in mass, charge, spin, and magnetic moment.

The photoelectric effect was first observed in 1887 by Heinrich Hertz during experiments with a spark gap generator (the earliest device that could be called a radio). In these experiments, sparks generated between two small metal spheres in a transmitter induce sparks that jump between between two different metal spheres in a receiver. Compared to later radio devices, the spark gap generator was notoriously difficult to work with. The air gap would often have to be smaller than a millimeter for a the receiver to reliably reproduce the spark of the transmitter. Hertz found that he could increase the sensitivity of his spark gap device by illuminating it with visible or ultraviolet light. Later studies by J.J. Thomson showed that this increased sensitivity was the result of light pushing on electrons — a particle that he discovered in 1897.

While this is interesting, it is hardly amazing. All forms of electromagnetic radiation transport energy and it is quite easy to imagine this energy being used to push tiny particles of negative charge free from the surface of a metal where they are not all that strongly confined in the first place. The era of modern physics is one of completely unexpected and inexplicable discoveries, however. Subsequent investigations into the photoelectric effect yielded results that did not fit with the classical theory of electromagnetic radiation. When it interacted with electrons, light just didn't behave like it was supposed to. Repairing this tear in theory required more than just a patch. It meant rebuilding a large portion of physics from the ground up.

It was Philipp Lenard , an assistant of Hertz, who performed the earliest, definitive studies of the photoelectric effect. Lenard used metal surfaces that were first cleaned and then held under a vacuum so that the effect might be studied on the metal alone and not be affected by any surface contaminants or oxidation. The metal sample was housed in an evacuated glass tube with a second metal plate mounted at the opposite end. The tube was then positioned or constrained in some manner so that light would only shine on the first metal plate — the one made out of photoemissive material under investigation. Such a tube is called a photocell (formally) or an electric eye (informally). Lenard connected his photocell to a circuit with a variable power supply, voltmeter, and microammeter as shown in the schematic diagram below. He then illuminated the photoemissive surface with light of differing frequencies and intensities.

Knocking electrons free from the photoemissive plate would give it a slight positive charge. Since the second plate was connected to the first by the wiring of the circuit, it too would become positive, which would then attract the photoelectrons floating freely through the vacuum where they would land and return back to the plate from which they started. Keep in mind that this experiment doesn't create electrons out of light, it just uses the energy in light to push electrons that are already there around the circuit. The photoelectric current generated by this means was quite small, but could be measured with the microammeter (a sensitive galvanometer with a maximum deflection of only a few microamps). It also serves as a measure of the rate at which photoelectrons are leaving the surface of the photoemissive material.

Note how the power supply is wired into the circuit — with its negative end connected to the plate that isn't illuminated. This sets up a potential difference that tries to push the photoelectrons back into the photoemissive surface. When the power supply is set to a low voltage it traps the least energetic electrons, reducing the current through the microammeter. Increasing the voltage drives increasingly more energetic electrons back until finally none of them are able to leave the metal surface and the microammeter reads zero. The potential at which this occurs is called the stopping potential . It is a measure of the maximum kinetic energy of the electrons emitted as a result of the photoelectric effect.

What Lenard found was that the intensity of the incident light had no effect on the maximum kinetic energy of the photoelectrons. Those ejected from exposure to a very bright light had the same energy as those ejected from exposure to a very dim light of the same frequency . In keeping with the law of conservation of energy, however, more electrons were ejected by a bright source than a dim source.

Later experiments by others, most notably the American physicist Robert Millikan in 1914, found that light with frequencies below a certain cutoff value, called the threshold frequency , would not eject photoelectrons from the metal surface no matter how bright the source was. These result were completely unexpected. Given that it is possible to move electrons with light and given that the energy in a beam of light is related to its intensity, classical physics would predict that a more intense beam of light would eject electrons with greater energy than a less intense beam no matter what the frequency . This was not the case, however.

Actually, maybe these results aren't all that typical. Most elements have threshold frequencies that are ultraviolet and only a few dip down low enough to be green or yellow like the example shown above. The materials with the lowest threshold frequencies are all semiconductors. Some have threshold frequencies in the infrared region of the spectrum.

The classical model of light describes it as a transverse, electromagnetic wave. Of this there was very little doubt at the end of the 19th century. The wave nature of light was confirmed when it was applied successfully to explain such optical phenomena as diffraction, interference, polarization, reflection and refraction. If we can imagine light as waves in an electromagnetic ocean and be quite successful at it, then it wouldn't be much of a stretch for us to image electrons in a metal surface as something like tethered buoys floating in an electromagnetic harbor. Along come the waves (light) which pull and tug at the buoys (electrons). Weak waves have no effect, but strong ones just might yank a buoy from their mooring and set it adrift. A wave model of light would predict an energy-amplitude relationship and not the energy-frequency relationship described above. Photoelectric experiments describe an electromagnetic ocean where monstrous swells wouldn't tip over a canoe, but tiny ripples would fling you into the air.

If that wasn't enough, the photoelectrons seem to pop out of the surface too quickly. When light intensities are very low, the rate at which energy is delivered to to the surface is downright sluggish. It should take a while for any one particular electron to capture enough of this diffuse energy to free itself. It should, but it doesn't. The instant that light with an appropriate frequency of any intensity strikes a photoemissive surface, at least one electron will always pop out immediately ( t  < 10 −9  s). Continuing with the ocean analogy, imagine a harbor full of small boats (electrons). The sea is calm except for tiny ripples on the surface (low intensity, short wavelength light). Most of the boats in the harbor are unaffected by these waves, but one is ripped from the harbor and sent flying upward like a jet aircraft. Something just ain't right here. No mechanical waves behave like this, but light does.

The two factors affecting maximum kinetic energy of photoelectrons are the frequency of the incident radiation and the material on the surface. As shown in the graph below, electron energy increases with frequency in a simple linear manner above the threshold. All three curves have the same slope (equal to Planck's constant ) which shows that the energy-frequency relation is constant for all materials. Below the threshold frequency photoemission does not occur. Each curve has a different intercept on the energy axis, which shows that threshold frequency is a function of the material.

The genius that figured out what was going on here was none other than the world's most famous physicist Albert Einstein . In 1905, Einstein realized that light was behaving as if it was composed of tiny particles (initially called quanta and later called photons ) and that the energy of each particle was proportional to the frequency of the electromagnetic radiation that it was a part of. Recall from the previous section of this book that Max Planck invented the notion of quantized electromagnetic radiation as a way to solve a technical problem with idealized sources of electromagnetic radiation called blackbodies. Recall also that Planck did not believe that radiation was actually broken up into little bits as his mathematical analysis showed. He thought the whole thing was just a contrivance that gave him the right answers. The genius of Einstein was in recognizing that Planck's contrivance was in fact a reasonable description of reality. What we perceive as a continuous wave of electromagnetic radiation is actually a stream of discrete particles.

Es scheint mir nun in der Tat, daß die Beobachtungen über die „schwarze Strahlung‟, Photolumineszenz, die Erzeugung von Kathodenstrahlen durch ultraviolettes Licht und andere die Erz­eu­gung bez. Verwandlung des Lichtes betreffende Erschein­ungs­gruppen besser verstandlich erscheinen unter der An­nahme, daß die Energie des Lichtes dis­kontinu­ier­lich im Raume verteilt sei. Nach der hier ins Auge zu fassenden Annahme ist bei Aus­brei­tung eines von einem Punkte aus­gehen­den Licht­strahles die Energie nicht kon­tinu­ier­lich auf größer und größer werden­cle Räume ver­teilt, sondvern es bes­teht dies­elbe aus einer end­li­chen Zahl von in Raum­punk­ten lokal­isier­ten Ener­gie­quan­ten, welche sich b­ewegen, ohne sich zu teil­en und nur als Ganze ab­sorb­iert und er­zeugt wer­den kön­nen. Albert Einstein, 1905 In fact, it seems to me that the observations on "black-body radiation", photoluminescence, the production of cathode rays by ultraviolet light and other phenomena involving the emission or conversion of light can be better understood on the assumption that the energy of light is distributed discontinuously in space. According to the assumption considered here, when a light ray starting from a point is propagated, the energy is not continuously distributed over an ever increasing volume, but it consists of a finite number of energy quanta, localized in space, which move without being divided and which can be absorbed or emitted only as a whole. Albert Einstein, 1905

Einstein and Millikan described the photoelectric effect using a formula (in contemporary notation) that relates the maximum kinetic energy ( K max ) of the photoelectrons to the frequency of the absorbed photons ( f ) and the threshold frequency ( f 0 ) of the photoemissive surface.

K max  =  h ( f  −  f 0 )

or if you prefer, to the energy of the absorbed photons ( E ) and the work function ( φ ) of the surface

K max  =  E  − φ

where the first term is the energy of the absorbed photons ( E ) with frequency ( f ) or wavelength ( λ )

and the second term is the work function ( φ ) of the surface with threshold frequency ( f 0 ) or threshold wavelength ( λ 0 )

The maximum kinetic energy ( K max ) of the photoelectrons (with charge e ) can be determined from the stopping potential ( V 0 ).

K max  =  eV 0

When charge ( e ) is given in coulombs, the energy will be calculated in joules. When charge ( e ) is given in elementary charges, the energy will be calculated in electron volts . This results in a lot of constants. Use the one that's most appropriate for your problem.

Lastly, the rate ( n / t ) at which photoelectrons (with charge e ) are emitted from a photoemissive surface can be determined from the photoelectric current ( I ).

• "electric eye", light meter, movie film audio track
• photoconductivity: an increase in the electrical conductivity of a nonmetallic solid when exposed the electromagnetic radiation. The increase in conductivity is due to the addition of free electrons liberated by collision with photons. The rate at which free electrons are generated and the time they over which the remain free determines the amount of the increase.
• photovoltaics: the ejected electron travels through the emitting material to enter a solid electrode in contact with the photoemitter (instead of traveling through a vacuum to an anode) leading to the direct conversion of radiant energy to electric energy
• photostatic copying

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Table of contents.

• Experiment 1 - Magnetic Fields of Coils and Faraday's Law
• Experiment 2 - Microwave Optics
• Experiment 3 - Geometrical Optics
• Experiment 4 - Physical Optics
• Experiment 5 - Fluids and Thermodynamics

Experiment 6 - The Photoelectric Effect

• Experiment 7 - Radioactivity
• Photodiode with amplifier
• Batteries to operate amplifier and provide reverse voltage
• Digital voltmeter to read reverse voltage
• Source of monochromatic light beams to irradiate photocathode
• Neutral filter to vary light intensity

INTRODUCTION

The energy quantization of electromagnetic radiation in general, and of light in particular, is expressed in the famous relation

\begin{eqnarray} E &=& hf, \label{eqn_1} \end{eqnarray}

where \(E\) is the energy of the radiation, \(f\) is its frequency, and \(h\) is Planck's constant (6.63×10 -34 Js). The notion of light quantization was first introduced by Planck. Its validity is based on solid experimental evidence, most notably the photoelectric effect . The basic physical process underlying this effect is the emission of electrons in metals exposed to light. There are four aspects of photoelectron emission which conflict with the classical view that the instantaneous intensity of electromagnetic radiation is given by the Poynting vector \(\textbf{S}\):

\begin{eqnarray} \textbf{S} &=& (\textbf{E}\times\textbf{B})/\mu_0, \label{eqn_2} \end{eqnarray}

with \(\textbf{E}\) and \(\textbf{B}\) the electric and magnetic fields of the radiation, respectively, and μ 0 (4π×10 -7 Tm/A) the permeability of free space. Specifically:

No photoelectrons are emitted from the metal when the incident light is below a minimum frequency, regardless of its intensity. (The value of the minimum frequency is unique to each metal.)

Photoelectrons are emitted from the metal when the incident light is above a threshold frequency. The kinetic energy of the emitted photoelectrons increases with the frequency of the light.

The number of emitted photoelectrons increases with the intensity of the incident light. However, the kinetic energy of these electrons is independent of the light intensity.

Photoemission is effectively instantaneous.

Consider the conduction electrons in a metal to be bound in a well-defined potential. The energy required to release an electron is called the work function \(W_0\) of the metal. In the classical model, a photoelectron could be released if the incident light had sufficient intensity. However, Eq. \eqref{eqn_1} requires that the light exceed a threshold frequency \(f_{\textrm{t}}\) for an electron to be emitted. If \(f > f_{\textrm{t}}\), then a single light quantum (called a photon ) of energy \(E = hf\) is sufficient to liberate an electron, and any residual energy carried by the photon is converted into the kinetic energy of the electron. Thus, from energy conservation, \(E = W_0 + K\), or

\begin{eqnarray} K &=& (1/2)mv^2 = E - W_0 = hf - W_0. \label{eqn_3} \end{eqnarray}

When the incident light intensity is increased, more photons are available for the release of electrons, and the magnitude of the photoelectric current increases. From Eq. \eqref{eqn_3}, we see that the kinetic energy of the electrons is independent of the light intensity and depends only on the frequency.

The photoelectric current in a typical setup is extremely small, and making a precise measurement is difficult. Normally the electrons will reach the anode of the photodiode, and their number can be measured from the (minute) anode current. However, we can apply a reverse voltage to the anode; this reverse voltage repels the electrons and prevents them from reaching the anode. The minimum required voltage is called the stopping potential \(V_{\textrm{s}}\), and the “stopping energy” of each electron is therefore \(eV_{\textrm{s}}\). Thus,

\begin{eqnarray} eV_{\textrm{s}} &=& hf - W_0, \label{eqn_4} \end{eqnarray}

\begin{eqnarray} V_{\textrm{s}} &=& (h/e)f - W_0/e. \label{eqn_5} \end{eqnarray}

Eq. \eqref{eqn_5} shows a linear relationship between the stopping potential \(V_{\textrm{s}}\) and the light frequency \(f\), with slope \(h/e\) and vertical intercept \(-W_0/e\). If the value of the electron charge \(e\) is known, then this equation provides a good method for determining Planck's constant \(h\). In this experiment, we will measure the stopping potential with modern electronics.

THE PHOTODIODE AND ITS READOUT

The central element of the apparatus is the photodiode tube. The diode has a window which allows light to enter, and the cathode is a clean metal surface. To prevent the collision of electrons with air molecules, the diode tube is evacuated.

The photodiode and its associated electronics have a small “capacitance” and develop a voltage as they become charged by the emitted electrons. When the voltage across this “capacitor” reaches the stopping potential of the cathode, the voltage difference between the cathode and anode (which is equal to the stopping potential) stabilizes.

To measure the stopping potential, we use a very sensitive amplifier which has an input impedance larger than 10 13 ohms. The amplifier enables us to investigate the minuscule number of photoelectrons that are produced.

It would take considerable time to discharge the anode at the completion of a measurement by the usual high-leakage resistance of the circuit components, as the input impedance of the amplifier is very high. To speed up this process, a shorting switch is provided; it is labeled “Push to Zero”. The amplifier output will not stay at 0 volts very long after the switch is released. However, the anode output does stabilize once the photoelectrons charge it up.

There are two 9-volt batteries already installed in the photodiode housing. To check the batteries, you can use a voltmeter to measure the voltage between the output ground terminal and each battery test terminal. The battery test points are located on the side panel. You should replace the batteries if the voltage is less than 6 volts.

THE MONOCHROMATIC LIGHT BEAMS

This experiment requires the use of several different monochromatic light beams, which can be obtained from the spectral lines that make up the radiation produced by excited mercury atoms. The light is formed by an electrical discharge in a thin glass tube containing mercury vapor, and harmful ultraviolet components are filtered out by the glass envelope. Mercury light has five narrow spectral lines in the visible region — yellow, green, blue, violet, and ultraviolet — which can be separated spatially by the process of diffraction. For this purpose, we use a high-quality diffraction grating with 6000 lines per centimeter. The desired wavelength is selected with the aid of a collimator, while the intensity can be varied with a set of neutral density filters. A color filter at the entrance of the photodiode is used to minimize room light.

The equipment consists of a mercury vapor light housed in a sturdy metal box, which also holds the transformer for the high voltage. The transformer is fed by a 115-volt power source from an ordinary wall outlet. In order to prevent the possibility of getting an electric shock from the high voltage, do not remove the cover from the unit when it is plugged in.

To facilitate mounting of the filters, the light box is equipped with rails on the front panel. The optical components include a fixed slit (called a light aperture) which is mounted over the output hole in the front cover of the light box. A lens focuses the aperture on the photodiode window. The diffraction grating is mounted on the same frame that holds the lens, which simplifies the setup somewhat. A “blazed” grating, which has a preferred orientation for maximal light transmission and is not fully symmetric, is used. Turn the grating around to verify that you have the optimal orientation.

The variable transmission filter consists of computer-generated patterns of dots and lines that vary the intensity of the incident light. The relative transmission percentages are 100%, 80%, 60%, 40%, and 20%.

INITIAL SETUP

Your apparatus should be set up approximately like the figure above. Turn on the mercury lamp using the switch on the back of the light box. Swing the \(h/e\) apparatus box around on its arm, and you should see at various positions, yellow green, and several blue spectral lines on its front reflective mask. Notice that on one side of the imaginary “front-on” perpendicular line from the mercury lamp, the spectral lines are brighter than the similar lines from the other side. This is because the grating is “blazed”. In you experiments, use the first order spectrum on the side with the brighter lines.

Your apparatus should already be approximately aligned from previous experiments, but make the following alignment checks. Ask you TA for assistance if necessary.

Check the alignment of the mercury source and the aperture by looking at the light shining on the back of the grating. If necessary, adjust the back plate of the light-aperture assembly by loosening the two retaining screws and moving the plate to the left or right until the light shines directly on the center of the grating.

With the bright colored lines on the front reflective mask, adjust the lens/grating assembly on the mercury lamp light box until the lines are focused as sharply as possible.

Roll the round light shield (between the white screen and the photodiode housing) out of the way to view the photodiode window inside the housing. The phototube has a small square window for light to enter. When a spectral line is centered on the front mask, it should also be centered on this window. If not, rotate the housing until the image of the aperture is centered on the window, and fasten the housing. Return the round shield back into position to block stray light.

Connect the digital voltmeter (DVM) to the “Output” terminals of the photodiode. Select the 2 V or 20 V range on the meter.

Press the “Push to Zero” button on the side panel of the photodiode housing to short out any accumulated charge on the electronics. Note that the output will shift in the absence of light on the photodiode.

Record the photodiode output voltage on the DVM. This voltage is a direct measure of the stopping potential.

Use the green and yellow filters for the green and yellow mercury light. These filters block higher frequencies and eliminate ambient room light. In higher diffraction orders, they also block the ultraviolet light that falls on top of the yellow and green lines.

PROCEDURE PART 1: DEPENDENCE OF THE STOPPING POTENTIAL ON THE INTENSITY OF LIGHT

Adjust the angle of the photodiode-housing assembly so that the green line falls on the window of the photodiode.

Install the green filter and the round light shield.

Install the variable transmission filter on the collimator over the green filter such that the light passes through the section marked 100%. Record the photodiode output voltage reading on the DVM. Also determine the approximate recharge time after the discharge button has been pressed and released.

Repeat steps 1 – 3 for the other four transmission percentages, as well as for the ultraviolet light in second order.

Plot a graph of the stopping potential as a function of intensity.

PROCEDURE PART 2: DEPENDENCE OF THE STOPPING POTENTIAL ON THE FREQUENCY OF LIGHT

You can see five colors in the mercury light spectrum. The diffraction grating has two usable orders for deflection on one side of the center.

Adjust the photodiode-housing assembly so that only one color from the first-order diffraction pattern on one side of the center falls on the collimator.

For each color in the first order, record the photodiode output voltage reading on the DVM.

For each color in the second order, record the photodiode output voltage reading on the DVM.

Plot a graph of the stopping potential as a function of frequency, and determine the slope and the \(y\)-intercept of the graph. From this data, calculate \(W_0\) and \(h\). Compare this value of \(h\) with that provided in the “Introduction” section of this experiment.

Procedure Part 1:

Photodiode output voltage reading for 100% transmission =                                              

Approximate recharge time for 100% transmission =                                              

Photodiode output voltage reading for 80% transmission =                                              

Approximate recharge time for 80% transmission =                                              

Photodiode output voltage reading for 60% transmission =                                              

Approximate recharge time for 60% transmission =                                              

Photodiode output voltage reading for 40% transmission =                                              

Approximate recharge time for 40% transmission =                                              

Photodiode output voltage reading for 20% transmission =                                              

Approximate recharge time for 20% transmission =                                              

Photodiode output voltage reading for ultraviolet light =                                              

Approximate recharge time for ultraviolet light =                                              

Plot the graph of stopping potential as a function of intensity using one sheet of graph paper at the end of this workbook. Remember to label the axes and title the graph.

Procedure Part 2:

First-order diffraction pattern on one side of the center:

Photodiode output voltage reading for yellow light =                                              

Photodiode output voltage reading for green light =                                              

Photodiode output voltage reading for blue light =                                              

Photodiode output voltage reading for violet light =                                              

Second-order diffraction pattern on the other side of the center:

Plot the graph of stopping potential as a function of frequency using one sheet of graph paper at the end of this workbook. Remember to label the axes and title the graph.

Slope of graph =                                              

\(y\)-intercept of graph =                                              

\(W_0\) =                                              

\(h\) =                                              

Percentage difference between experimental and accepted values of \(h\) =                

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Chapter 29 Introduction to Quantum Physics

29.2 The Photoelectric Effect

• Describe a typical photoelectric-effect experiment.
• Determine the maximum kinetic energy of photoelectrons ejected by photons of one energy or wavelength, when given the maximum kinetic energy of photoelectrons for a different photon energy or wavelength.

When light strikes materials, it can eject electrons from them. This is called the photoelectric effect , meaning that light ( photo ) produces electricity. One common use of the photoelectric effect is in light meters, such as those that adjust the automatic iris on various types of cameras. In a similar way, another use is in solar cells, as you probably have in your calculator or have seen on a roof top or a roadside sign. These make use of the photoelectric effect to convert light into electricity for running different devices.

This effect has been known for more than a century and can be studied using a device such as that shown in Figure 1 . This figure shows an evacuated tube with a metal plate and a collector wire that are connected by a variable voltage source, with the collector more negative than the plate. When light (or other EM radiation) strikes the plate in the evacuated tube, it may eject electrons. If the electrons have energy in electron volts (eV) greater than the potential difference between the plate and the wire in volts, some electrons will be collected on the wire. Since the electron energy in eV is [latex]{qV}[/latex], where [latex]{q}[/latex] is the electron charge and [latex]{V}[/latex] is the potential difference, the electron energy can be measured by adjusting the retarding voltage between the wire and the plate. The voltage that stops the electrons from reaching the wire equals the energy in eV. For example, if [latex]{-3.00 V}[/latex] barely stops the electrons, their energy is 3.00 eV. The number of electrons ejected can be determined by measuring the current between the wire and plate. The more light, the more electrons; a little circuitry allows this device to be used as a light meter.

What is really important about the photoelectric effect is what Albert Einstein deduced from it. Einstein realized that there were several characteristics of the photoelectric effect that could be explained only if EM radiation is itself quantized : the apparently continuous stream of energy in an EM wave is actually composed of energy quanta called photons. In his explanation of the photoelectric effect, Einstein defined a quantized unit or quantum of EM energy, which we now call a photon , with an energy proportional to the frequency of EM radiation. In equation form, the photon energy is

where [latex]{E}[/latex] is the energy of a photon of frequency [latex]{f}[/latex] and [latex]{h}[/latex] is Planck’s constant. This revolutionary idea looks similar to Planck’s quantization of energy states in blackbody oscillators, but it is quite different. It is the quantization of EM radiation itself. EM waves are composed of photons and are not continuous smooth waves as described in previous chapters on optics. Their energy is absorbed and emitted in lumps, not continuously. This is exactly consistent with Planck’s quantization of energy levels in blackbody oscillators, since these oscillators increase and decrease their energy in steps of [latex]{hf}[/latex] by absorbing and emitting photons having [latex]{E = hf}[/latex]. We do not observe this with our eyes, because there are so many photons in common light sources that individual photons go unnoticed. (See Figure 2 .) The next section of the text (

Chapter 29.3 Photon Energies and the Electromagnetic Spectrum ) is devoted to a discussion of photons and some of their characteristics and implications. For now, we will use the photon concept to explain the photoelectric effect, much as Einstein did.

The photoelectric effect has the properties discussed below. All these properties are consistent with the idea that individual photons of EM radiation are absorbed by individual electrons in a material, with the electron gaining the photon’s energy. Some of these properties are inconsistent with the idea that EM radiation is a simple wave. For simplicity, let us consider what happens with monochromatic EM radiation in which all photons have the same energy [latex]{hf}[/latex].

• If we vary the frequency of the EM radiation falling on a material, we find the following: For a given material, there is a threshold frequency [latex]{f_0}[/latex] for the EM radiation below which no electrons are ejected, regardless of intensity. Individual photons interact with individual electrons. Thus if the photon energy is too small to break an electron away, no electrons will be ejected. If EM radiation was a simple wave, sufficient energy could be obtained by increasing the intensity.
• Once EM radiation falls on a material, electrons are ejected without delay . As soon as an individual photon of a sufficiently high frequency is absorbed by an individual electron, the electron is ejected. If the EM radiation were a simple wave, several minutes would be required for sufficient energy to be deposited to the metal surface to eject an electron.
• The number of electrons ejected per unit time is proportional to the intensity of the EM radiation and to no other characteristic. High-intensity EM radiation consists of large numbers of photons per unit area, with all photons having the same characteristic energy [latex]{hf}[/latex].
• If we vary the intensity of the EM radiation and measure the energy of ejected electrons, we find the following: The maximum kinetic energy of ejected electrons is independent of the intensity of the EM radiation . Since there are so many electrons in a material, it is extremely unlikely that two photons will interact with the same electron at the same time, thereby increasing the energy given it. Instead (as noted in 3 above), increased intensity results in more electrons of the same energy being ejected. If EM radiation were a simple wave, a higher intensity could give more energy, and higher-energy electrons would be ejected.

where [latex]{\text{KE}_e}[/latex] is the maximum kinetic energy of the ejected electron, [latex]{hf}[/latex] is the photon’s energy, and BE is the binding energy of the electron to the particular material. (BE is sometimes called the work function of the material.) This equation, due to Einstein in 1905, explains the properties of the photoelectric effect quantitatively. An individual photon of EM radiation (it does not come any other way) interacts with an individual electron, supplying enough energy, BE, to break it away, with the remainder going to kinetic energy. The binding energy is [latex]{\text{BE} = hf_0}[/latex], where [latex]{f_0}[/latex] is the threshold frequency for the particular material. Figure 3 shows a graph of maximum [latex]{\text{KE}_e}[/latex] versus the frequency of incident EM radiation falling on a particular material.

Einstein’s idea that EM radiation is quantized was crucial to the beginnings of quantum mechanics. It is a far more general concept than its explanation of the photoelectric effect might imply. All EM radiation can also be modeled in the form of photons, and the characteristics of EM radiation are entirely consistent with this fact. (As we will see in the next section, many aspects of EM radiation, such as the hazards of ultraviolet (UV) radiation, can be explained only by photon properties.) More famous for modern relativity, Einstein planted an important seed for quantum mechanics in 1905, the same year he published his first paper on special relativity. His explanation of the photoelectric effect was the basis for the Nobel Prize awarded to him in 1921. Although his other contributions to theoretical physics were also noted in that award, special and general relativity were not fully recognized in spite of having been partially verified by experiment by 1921. Although hero-worshipped, this great man never received Nobel recognition for his most famous work—relativity.

Example 1: Calculating Photon Energy and the Photoelectric Effect: A Violet Light

(a) What is the energy in joules and electron volts of a photon of 420-nm violet light? (b) What is the maximum kinetic energy of electrons ejected from calcium by 420-nm violet light, given that the binding energy (or work function) of electrons for calcium metal is 2.71 eV?

To solve part (a), note that the energy of a photon is given by [latex]{E = hf}[/latex]. For part (b), once the energy of the photon is calculated, it is a straightforward application of [latex]{\text{KE}_e = hf - \text{BE}}[/latex] to find the ejected electron’s maximum kinetic energy, since BE is given.

Solution for (a)

Photon energy is given by

Since we are given the wavelength rather than the frequency, we solve the familiar relationship [latex]{c = \frac{f}{\lambda}}[/latex] for the frequency, yielding

Combining these two equations gives the useful relationship

Now substituting known values yields

Converting to eV, the energy of the photon is

Solution for (b)

Finding the kinetic energy of the ejected electron is now a simple application of the equation [latex]{\text{KE}_e = hf - \text{BE}}[/latex]. Substituting the photon energy and binding energy yields

The energy of this 420-nm photon of violet light is a tiny fraction of a joule, and so it is no wonder that a single photon would be difficult for us to sense directly—humans are more attuned to energies on the order of joules. But looking at the energy in electron volts, we can see that this photon has enough energy to affect atoms and molecules. A DNA molecule can be broken with about 1 eV of energy, for example, and typical atomic and molecular energies are on the order of eV, so that the UV photon in this example could have biological effects. The ejected electron (called a photoelectron ) has a rather low energy, and it would not travel far, except in a vacuum. The electron would be stopped by a retarding potential of but 0.26 eV. In fact, if the photon wavelength were longer and its energy less than 2.71 eV, then the formula would give a negative kinetic energy, an impossibility. This simply means that the 420-nm photons with their 2.96-eV energy are not much above the frequency threshold. You can show for yourself that the threshold wavelength is 459 nm (blue light). This means that if calcium metal is used in a light meter, the meter will be insensitive to wavelengths longer than those of blue light. Such a light meter would be completely insensitive to red light, for example.

PhET Explorations: Photoelectric Effect

See how light knocks electrons off a metal target, and recreate the experiment that spawned the field of quantum mechanics.

Section Summary

• The photoelectric effect is the process in which EM radiation ejects electrons from a material.
• Einstein proposed photons to be quanta of EM radiation having energy [latex]{E = hf}[/latex], where [latex]{f}[/latex] is the frequency of the radiation.
• All EM radiation is composed of photons. As Einstein explained, all characteristics of the photoelectric effect are due to the interaction of individual photons with individual electrons.
• The maximum kinetic energy [latex]{\text{KE}_e}[/latex] of ejected electrons (photoelectrons) is given by [latex]{\text{KE}_e = hf - \text{BE}}[/latex], where [latex]{hf}[/latex] is the photon energy and BE is the binding energy (or work function) of the electron to the particular material.

Conceptual Questions

1: Is visible light the only type of EM radiation that can cause the photoelectric effect?

2: Which aspects of the photoelectric effect cannot be explained without photons? Which can be explained without photons? Are the latter inconsistent with the existence of photons?

3: Is the photoelectric effect a direct consequence of the wave character of EM radiation or of the particle character of EM radiation? Explain briefly.

4: Insulators (nonmetals) have a higher BE than metals, and it is more difficult for photons to eject electrons from insulators. Discuss how this relates to the free charges in metals that make them good conductors.

5: If you pick up and shake a piece of metal that has electrons in it free to move as a current, no electrons fall out. Yet if you heat the metal, electrons can be boiled off. Explain both of these facts as they relate to the amount and distribution of energy involved with shaking the object as compared with heating it.

Problems & Exercises

1: What is the longest-wavelength EM radiation that can eject a photoelectron from silver, given that the binding energy is 4.73 eV? Is this in the visible range?

2: Find the longest-wavelength photon that can eject an electron from potassium, given that the binding energy is 2.24 eV. Is this visible EM radiation?

3: What is the binding energy in eV of electrons in magnesium, if the longest-wavelength photon that can eject electrons is 337 nm?

4: Calculate the binding energy in eV of electrons in aluminum, if the longest-wavelength photon that can eject them is 304 nm.

5: What is the maximum kinetic energy in eV of electrons ejected from sodium metal by 450-nm EM radiation, given that the binding energy is 2.28 eV?

6: UV radiation having a wavelength of 120 nm falls on gold metal, to which electrons are bound by 4.82 eV. What is the maximum kinetic energy of the ejected photoelectrons?

7: Violet light of wavelength 400 nm ejects electrons with a maximum kinetic energy of 0.860 eV from sodium metal. What is the binding energy of electrons to sodium metal?

8: UV radiation having a 300-nm wavelength falls on uranium metal, ejecting 0.500-eV electrons. What is the binding energy of electrons to uranium metal?

9: What is the wavelength of EM radiation that ejects 2.00-eV electrons from calcium metal, given that the binding energy is 2.71 eV? What type of EM radiation is this?

10: Find the wavelength of photons that eject 0.100-eV electrons from potassium, given that the binding energy is 2.24 eV. Are these photons visible?

11: What is the maximum velocity of electrons ejected from a material by 80-nm photons, if they are bound to the material by 4.73 eV?

12: Photoelectrons from a material with a binding energy of 2.71 eV are ejected by 420-nm photons. Once ejected, how long does it take these electrons to travel 2.50 cm to a detection device?

13: A laser with a power output of 2.00 mW at a wavelength of 400 nm is projected onto calcium metal. (a) How many electrons per second are ejected? (b) What power is carried away by the electrons, given that the binding energy is 2.71 eV?

14: (a) Calculate the number of photoelectrons per second ejected from a 1.00-mm 2 area of sodium metal by 500-nm EM radiation having an intensity of [latex]{1.30 \;\text{kW/m}^2}[/latex] (the intensity of sunlight above the Earth’s atmosphere). (b) Given that the binding energy is 2.28 eV, what power is carried away by the electrons? (c) The electrons carry away less power than brought in by the photons. Where does the other power go? How can it be recovered?

15: Unreasonable Results

Red light having a wavelength of 700 nm is projected onto magnesium metal to which electrons are bound by 3.68 eV. (a) Use [latex]{\text{KE}_e = hf - \text{BE}}[/latex] to calculate the kinetic energy of the ejected electrons. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

16: Unreasonable Results

(a) What is the binding energy of electrons to a material from which 4.00-eV electrons are ejected by 400-nm EM radiation? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

5: 0.483 eV

9: (a) 264 nm

(b) Ultraviolet

11:  [latex]{1.95 \times 10^6 \;\text{m/s}}[/latex]

13: (a) [latex]{4.02 \times 10^{15} \text{/s}}[/latex]

(b) 0.256 mW

15: (a) [latex]{-1.90 \;\text{eV}}[/latex]

(b) Negative kinetic energy

(c) That the electrons would be knocked free.

College Physics Copyright © August 22, 2016 by OpenStax is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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21.2 Einstein and the Photoelectric Effect

Section learning objectives.

By the end of this section, you will be able to do the following:

• Describe Einstein’s explanation of the photoelectric effect
• Describe how the photoelectric effect could not be explained by classical physics
• Calculate the energy of a photoelectron under given conditions
• Describe use of the photoelectric effect in biological applications, photoelectric devices and movie soundtracks

Teacher Support

The learning objectives in this section will help your students master the following standards:

• (D) : explain the impacts of the scientific contributions of a variety of historical and contemporary scientists on scientific thought and society.
• (A) : describe the photoelectric effect and the dual nature of light.

Section Key Terms

The Photoelectric Effect

[EL]Ask the students what they think the term photoelectric means. How does the term relate to its definition?

When light strikes certain materials, it can eject electrons from them. This is called the photoelectric effect , meaning that light ( photo ) produces electricity. One common use of the photoelectric effect is in light meters, such as those that adjust the automatic iris in various types of cameras. Another use is in solar cells, as you probably have in your calculator or have seen on a rooftop or a roadside sign. These make use of the photoelectric effect to convert light into electricity for running different devices.

[BL] [OL] Discuss with students what may cause light to eject electrons from a material. Are there certain materials that are more susceptible to having electrons ejected?

[AL] Ask students why a light meter would be useful in a camera. How could the number of electrons emitted from the light meter control the camera’s iris? Have students draw a diagram of the camera that may demonstrate this effect.

Revolutionary Properties of the Photoelectric Effect

When Max Planck theorized that energy was quantized in a blackbody radiator, it is unlikely that he would have recognized just how revolutionary his idea was. Using tools similar to the light meter in Figure 21.5 , it would take a scientist of Albert Einstein ’s stature to fully discover the implications of Max Planck’s radical concept.

Through careful observations of the photoelectric effect, Albert Einstein realized that there were several characteristics that could be explained only if EM radiation is itself quantized . While these characteristics will be explained a bit later in this section, you can already begin to appreciate why Einstein’s idea is very important. It means that the apparently continuous stream of energy in an EM wave is actually not a continuous stream at all. In fact, the EM wave itself is actually composed of tiny quantum packets of energy called photons .

In equation form, Einstein found the energy of a photon or photoelectron to be

where E is the energy of a photon of frequency f and h is Planck’s constant. A beam from a flashlight, which to this point had been considered a wave, instead could now be viewed as a series of photons, each providing a specific amount of energy see Figure 21.6 . Furthermore, the amount of energy within each individual photon is based upon its individual frequency, as dictated by E = h f . E = h f . As a result, the total amount of energy provided by the beam could now be viewed as the sum of all frequency-dependent photon energies added together.

It is important for students to be comfortable with the material to this point before moving forward. To ensure that they are, one task that you may have them do is to draw a few pictures similar to Figure 21.6 . Have the students draw photons leaving a low intensity flashlight vs. a high intensity flashlight, a high frequency flashlight vs. a low frequency flashlight, and a high wavelength flashlight vs. a low wavelength flashlight. These diagrams will help ensure the students understand fundamental concepts before moving to the difficult proofs that follow.

Just as with Planck’s blackbody radiation, Einstein’s concept of the photon could take hold in the scientific community only if it could succeed where classical physics failed. The photoelectric effect would be a key to demonstrating Einstein’s brilliance.

Consider the following five properties of the photoelectric effect. All of these properties are consistent with the idea that individual photons of EM radiation are absorbed by individual electrons in a material, with the electron gaining the photon’s energy. Some of these properties are inconsistent with the idea that EM radiation is a simple wave. For simplicity, let us consider what happens with monochromatic EM radiation in which all photons have the same energy hf .

• If we vary the frequency of the EM radiation falling on a clean metal surface, we find the following: For a given material, there is a threshold frequency f 0 for the EM radiation below which no electrons are ejected, regardless of intensity. Using the photon model, the explanation for this is clear. Individual photons interact with individual electrons. Thus if the energy of an individual photon is too low to break an electron away, no electrons will be ejected. However, if EM radiation were a simple wave, sufficient energy could be obtained simply by increasing the intensity.
• Once EM radiation falls on a material, electrons are ejected without delay . As soon as an individual photon of sufficiently high frequency is absorbed by an individual electron, the electron is ejected. If the EM radiation were a simple wave, several minutes would be required for sufficient energy to be deposited at the metal surface in order to eject an electron.
• The number of electrons ejected per unit time is proportional to the intensity of the EM radiation and to no other characteristic. High-intensity EM radiation consists of large numbers of photons per unit area, with all photons having the same characteristic energy, hf . The increased number of photons per unit area results in an increased number of electrons per unit area ejected.
• If we vary the intensity of the EM radiation and measure the energy of ejected electrons, we find the following: The maximum kinetic energy of ejected electrons is independent of the intensity of the EM radiation . Instead, as noted in point 3 above, increased intensity results in more electrons of the same energy being ejected. If EM radiation were a simple wave, a higher intensity could transfer more energy, and higher-energy electrons would be ejected.
• The kinetic energy KE of an ejected electron equals the photon energy minus the binding energy BE of the electron in the specific material. An individual photon can give all of its energy to an electron. The photon’s energy is partly used to break the electron away from the material. The remainder goes into the ejected electron’s kinetic energy. In equation form, this is given by

where K E e K E e is the maximum kinetic energy of the ejected electron, h f h f is the photon’s energy, and BE is the binding energy of the electron to the particular material. The binding energy is also often called the work function of the material. This equation explains the properties of the photoelectric effect quantitatively and demonstrates that BE is the minimum amount of energy necessary to eject an electron. If the energy supplied is less than BE, the electron cannot be ejected. The binding energy can also be written as B E = h f 0 , B E = h f 0 , where f 0 f 0 is the threshold frequency for the particular material. Figure 21.8 shows a graph of maximum K E e K E e versus the frequency of incident EM radiation falling on a particular material.

Show students Figure 21.8 . What would be the kinetic energy of an electron if f is less than f 0 ? What does this mean? Why would this be the case? These questions aim to help students internalize the concept of binding energy.

Tips For Success

The following five pieces of information can be difficult to follow without some organization. It may be useful to create a table of expected results of each of the five properties, with one column showing the classical wave model result and one column showing the modern photon model result.

The table may look something like Table 21.1

It may be useful to complete the table above as a class. This material takes some time to interpret, so encourage students to move slowly. Once completed, your table may look like Table 21.2 .

Virtual Physics

Photoelectric effect.

In this demonstration, see how light knocks electrons off a metal target, and recreate the experiment that spawned the field of quantum mechanics.

Grasp Check

In the circuit provided, what are the three ways to increase the current?

• increase the intensity, increase the wavelength, alter the target
• decrease the intensity, increase the wavelength, alter the target
• decrease the intensity, decrease the wavelength, alter the target
• increase the intensity, decrease the wavelength, alter the target

Worked Example

Photon energy and the photoelectric effect: a violet light.

(a) What is the energy in joules and electron volts of a photon of 420-nm violet light? (b) What is the maximum kinetic energy of electrons ejected from calcium by 420 nm violet light, given that the binding energy of electrons for calcium metal is 2.71 eV?

To solve part (a), note that the energy of a photon is given by E = h f E = h f . For part (b), once the energy of the photon is calculated, it is a straightforward application of K E e = h f − B E K E e = h f − B E to find the ejected electron’s maximum kinetic energy, since BE is given.

Photon energy is given by

E = h f . E = h f .

Since we are given the wavelength rather than the frequency, we solve the familiar relationship c = f λ c = f λ for the frequency, yielding

Combining these two equations gives the useful relationship

Now substituting known values yields

Converting to eV, the energy of the photon is

Finding the kinetic energy of the ejected electron is now a simple application of the equation K E e = h f − B E K E e = h f − B E . Substituting the photon energy and binding energy yields

The energy of this 420 nm photon of violet light is a tiny fraction of a joule, and so it is no wonder that a single photon would be difficult for us to sense directly—humans are more attuned to energies on the order of joules. But looking at the energy in electron volts, we can see that this photon has enough energy to affect atoms and molecules. A DNA molecule can be broken with about 1 eV of energy, for example, and typical atomic and molecular energies are on the order of eV, so that the photon in this example could have biological effects, such as sunburn. The ejected electron has rather low energy, and it would not travel far, except in a vacuum. The electron would be stopped by a retarding potential of only 0.26 eV, a slightly larger KE than calculated above. In fact, if the photon wavelength were longer and its energy less than 2.71 eV, then the formula would give a negative kinetic energy, an impossibility. This simply means that the 420 nm photons with their 2.96 eV energy are not much above the frequency threshold. You can see for yourself that the threshold wavelength is 458 nm (blue light). This means that if calcium metal were used in a light meter, the meter would be insensitive to wavelengths longer than those of blue light. Such a light meter would be completely insensitive to red light, for example.

Practice Problems

What is the longest-wavelength EM radiation that can eject a photoelectron from silver, given that the bonding energy is 4.73 eV ? Is this radiation in the visible range?

• 2.63 × 10 −7 m; No, the radiation is in microwave region.
• 2.63 × 10 −7 m; No, the radiation is in visible region.
• 2.63 × 10 −7 m; No, the radiation is in infrared region.
• 2.63 × 10 -7 m; No, the radiation is in ultraviolet region.

What is the maximum kinetic energy in eV of electrons ejected from sodium metal by 450-nm EM radiation, given that the binding energy is 2.28 eV?

Technological Applications of the Photoelectric Effect

While Einstein’s understanding of the photoelectric effect was a transformative discovery in the early 1900s, its presence is ubiquitous today. If you have watched streetlights turn on automatically in response to the setting sun, stopped elevator doors from closing simply by putting your hands between them, or turned on a water faucet by sliding your hands near it, you are familiar with the electric eye , a name given to a group of devices that use the photoelectric effect for detection.

All these devices rely on photoconductive cells. These cells are activated when light is absorbed by a semi-conductive material, knocking off a free electron. When this happens, an electron void is left behind, which attracts a nearby electron. The movement of this electron, and the resultant chain of electron movements, produces a current. If electron ejection continues, further holes are created, thereby increasing the electrical conductivity of the cell. This current can turn switches on and off and activate various familiar mechanisms.

One such mechanism takes place where you may not expect it. Next time you are at the movie theater, pay close attention to the sound coming out of the speakers. This sound is actually created using the photoelectric effect! The audiotape in the projector booth is a transparent piece of film of varying width. This film is fed between a photocell and a bright light produced by an exciter lamp. As the transparent portion of the film varies in width, the amount of light that strikes the photocell varies as well. As a result, the current in the photoconductive circuit changes with the width of the filmstrip. This changing current is converted to a changing frequency, which creates the soundtrack commonly heard in the theater.

Work In Physics

Solar energy physicist.

According to the U.S. Department of Energy, Earth receives enough sunlight each hour to power the entire globe for a year. While converting all of this energy is impossible, the job of the solar energy physicist is to explore and improve upon solar energy conversion technologies so that we may harness more of this abundant resource.

The field of solar energy is not a new one. For over half a century, satellites and spacecraft have utilized photovoltaic cells to create current and power their operations. As time has gone on, scientists have worked to adapt this process so that it may be used in homes, businesses, and full-scale power stations using solar cells like the one shown in Figure 21.9 .

Solar energy is converted to electrical energy in one of two manners: direct transfer through photovoltaic cells or thermal conversion through the use of a CSP, concentrating solar power, system. Unlike electric eyes, which trip a mechanism when current is lost, photovoltaic cells utilize semiconductors to directly transfer the electrons released through the photoelectric effect into a directed current. The energy from this current can then be converted for storage, or immediately used in an electric process. A CSP system is an indirect method of energy conversion. In this process, light from the Sun is channeled using parabolic mirrors. The light from these mirrors strikes a thermally conductive material, which then heats a pool of water. This water, in turn, is converted to steam, which turns a turbine and creates electricity. While indirect, this method has long been the traditional means of large-scale power generation.

There are, of course, limitations to the efficacy of solar power. Cloud cover, nightfall, and incident angle strike at high altitudes are all factors that directly influence the amount of light energy available. Additionally, the creation of photovoltaic cells requires rare-earth minerals that can be difficult to obtain. However, the major role of a solar energy physicist is to find ways to improve the efficiency of the solar energy conversion process. Currently, this is done by experimenting with new semi conductive materials, by refining current energy transfer methods, and by determining new ways of incorporating solar structures into the current power grid.

Additionally, many solar physicists are looking into ways to allow for increased solar use in impoverished, more remote locations. Because solar energy conversion does not require a connection to a large-scale power grid, research into thinner, more mobile materials will permit remote cultures to use solar cells to convert sunlight collected during the day into stored energy that can then be used at night.

Regardless of the application, solar energy physicists are an important part of the future in responsible energy growth. While a doctoral degree is often necessary for advanced research applications, a bachelor's or master's degree in a related science or engineering field is typically enough to gain access into the industry. Computer skills are very important for energy modeling, including knowledge of CAD software for design purposes. In addition, the ability to collaborate and communicate with others is critical to becoming a solar energy physicist.

What role does the photoelectric effect play in the research of a solar energy physicist?

• The understanding of photoelectric effect allows the physicist to understand the generation of light energy when using photovoltaic cells.
• The understanding of photoelectric effect allows the physicist to understand the generation of electrical energy when using photovoltaic cells.
• The understanding of photoelectric effect allows the physicist to understand the generation of electromagnetic energy when using photovoltaic cells.
• The understanding of photoelectric effect allows the physicist to understand the generation of magnetic energy when using photovoltaic cells.

Check Your Understanding

• A beam of light energy is now considered a continual stream of wave energy, not photons.
• A beam of light energy is now considered a collection of photons, each carrying its own individual energy.

True or false—Visible light is the only type of electromagnetic radiation that can cause the photoelectric effect.

• The photoelectric effect is a direct consequence of the particle nature of EM radiation.
• The photoelectric effect is a direct consequence of the wave nature of EM radiation.
• The photoelectric effect is a direct consequence of both the wave and particle nature of EM radiation.
• The photoelectric effect is a direct consequence of neither the wave nor the particle nature of EM radiation.

Which aspects of the photoelectric effect can only be explained using photons?

• aspects 1, 2, and 3
• aspects 1, 2, and 4
• aspects 1, 2, 4 and 5
• aspects 1, 2, 3, 4 and 5
• Solar energy transforms into electric energy.
• Solar energy transforms into mechanical energy.
• Solar energy transforms into thermal energy.
• In a photovoltaic cell, thermal energy transforms into electric energy.

True or false—A current is created in a photoconductive cell, even if only one electron is expelled from a photon strike.

• A photon is a quantum packet of energy; it has infinite mass.
• A photon is a quantum packet of energy; it is massless.
• A photon is a fundamental particle of an atom; it has infinite mass.
• A photon is a fundamental particle of an atom; it is massless.

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Photoelectric Effect: Definition, Equation & Experiment

Everything learned in classical physics was turned on its head as physicists explored ever smaller realms and discovered quantum effects. Among the first of these discoveries was the photoelectric effect. In the early 1900s, the results of this effect failed to match classical predictions and were only explainable with quantum theory, opening up a whole new world for physicists.

Today, the photoelectric effect has many practical applications as well. From medical imaging to the production of clean energy, the discovery and application of this effect now has implications that go well beyond simply understanding the science.

What Is the Photoelectric Effect?

When light, or electromagnetic radiation, hits a material such as a metal surface, that material sometimes emits electrons, called ​ photoelectrons ​. This is essentially because the atoms in the material are absorbing the radiation as energy. Electrons in atoms absorb radiation by jumping to higher energy levels. If the energy absorbed is high enough, the electrons leave their home atom entirely.

This process is sometimes also called ​ photoemission ​ because incident photons (another name for particles of light) are the direct cause of the emission of electrons. Because electrons have a negative charge, the metal plate from which they were emitted is left ionized.

What was most special about the photoelectric effect, however, was that it did not follow classical predictions. The way in which the electrons were emitted, the number that were emitted and how this changed with intensity of light all left scientists scratching their heads initially.

Original Predictions

The original predictions as to the results of the photoelectric effect made from classical physics included the following:

• Energy transfers from incident radiation to the electrons. It was assumed that whatever energy is incident upon the material would be directly absorbed by the electrons in the atoms, regardless of wavelength. This makes sense in the classical mechanics paradigm: Whatever you pour into the bucket fills the bucket by that amount.
• Changes in light intensity should yield changes in kinetic energy of electrons. If it is assumed that electrons are absorbing whatever radiation is incident upon them, then more of the same radiation should give them more energy accordingly. Once the electrons have left the bounds of their atoms, that energy is seen in the form of kinetic energy.
• Very low-intensity light should yield a time lag between light absorption and emission of electrons. This would be because it was assumed that electrons must gain enough energy to leave their home atom, and low-intensity light is like adding energy to their energy “bucket” more slowly. It takes longer to fill, and hence it should take longer before the electrons have enough energy to be emitted.

Actual Results

The actual results were not at all consistent with the predictions. This included the following:

• Electrons were released only when the incident light reached or exceeded a threshold frequency. No emission occurred below that frequency. It didn’t matter if the intensity was high or low. For some reason, the frequency, or wavelength of the light itself, was much more important. 
• Changes in intensity did not yield changes in kinetic energy of electrons. They changed only the number of electrons emitted. Once the threshold frequency was reached, increasing the intensity did not add more energy to each emitted electron at all. Instead, they all ended up with the same kinetic energy; there were just more of them.
• There was no time lag at low intensities. There seemed to be no time required to “fill the energy bucket” of any given electron. If an electron was to be emitted, it was emitted immediately. Lower intensity had no effect on kinetic energy or lag time; it simply resulted in fewer electrons being emitted. 

Photoelectric Effect Explained

The only way to explain this phenomenon was to invoke quantum mechanics. Think of a beam of light not as a wave, but as a collection of discrete wave packets called photons. The photons all have distinct energy values that correspond to the frequency and wavelength of the light, as explained by wave-particle duality.

In addition, consider that the electrons are only able to jump between discrete energy states. They can only have specific energy values, but never any values in between. Now the observed phenomena can be explained as follows:

• Electrons are released only when they absorb very specific sufficient energy values. Any electron that gets the right energy packet (photon energy) will be released. None are released if the frequency of the incident light is too low regardless of intensity because none of the energy packets are individually big enough. 
• Once the threshold frequency is exceeded, increasing intensity only increases the number of electrons released and not the energy of the electrons themselves because each emitted electron absorbs one discrete photon. Greater intensity means more photons, and hence more photoelectrons. 
• There is no time delay even at low intensity as long as the frequency is high enough because as soon as an electron gets the right energy packet, it is released. Low intensity only results in fewer electrons.

The Work Function

One important concept related to the photoelectric effect is the work function. Also known as electron-binding energy, it is the minimum energy needed to remove an electron from a solid.

The formula for the work function is given by:

Where ​ -e ​ is the electron charge, ​ ϕ ​ is the electrostatic potential in the vacuum nearby the surface and ​ E ​ is the Fermi level of electrons in the material.

Electrostatic potential is measured in volts and is a measure of the electric potential energy per unit charge. Hence the first term in the expression, ​ -eϕ ​, is the electric potential energy of an electron near the surface of the material.

The Fermi level can be thought of as the energy of the outermost electron when the atom is in its ground state.

Threshold Frequency

Closely related to the work function is the threshold frequency. This is the minimum frequency at which incident photons will cause the emission of electrons. Frequency is directly related to energy (higher frequency corresponds to higher energy), hence why a minimum frequency must be reached.

Above the threshold frequency, the kinetic energy of the electrons depends on the frequency and not the intensity of the light. Basically the energy of a single photon will be transferred entirely to a single electron. A certain amount of that energy is used to eject the electron, and the remainder is its kinetic energy. Again, a greater intensity just means more electrons will be emitted, not that those emitted will have any more energy.

The maximum kinetic energy of emitted electrons can be found via the following equation:

Where ​ K max ​ is the maximum kinetic energy of the photoelectron, ​ h ​ is Planck's constant = 6.62607004 ×10 -34 m 2 kg/s, ​ f ​ is the frequency of the light and ​ f 0 ​ is the threshold frequency.

Discovery of the Photoelectric Effect

You can think of the discovery of the photoelectric effect as happening in two stages. First, the discovery of the emission of photoelectrons from certain materials as a result of incident light, and second, the determination that this effect does not obey classical physics at all, which led to many important underpinnings of our understanding of quantum mechanics.

Heinrich Hertz first observed the photoelectric effect in 1887 while performing experiments with a spark gap generator. The setup involved two pairs of metal spheres. Sparks generated between the first set of spheres would induce sparks to jump between the second set, thus acting as transducer and receiver. Hertz was able to increase the sensitivity of the setup by shining light on it. Years later, J.J. Thompson discovered that the increased sensitivity resulted from the light causing the electrons to be ejected.

While Hertz’s assistant Phillip Lenard determined that the intensity did not affect the kinetic energy of the photoelectrons, it was Robert Millikan who discovered the threshold frequency. Later, Einstein was able to explain the strange phenomenon by assuming the quantization of energy.

Importance of the Photoelectric Effect

Albert Einstein was awarded the Nobel Prize in 1921 for his discovery of the law of the photoelectric effect, and Millikan won the Nobel Prize in 1923 also for work related to understanding the photoelectric effect.

The photoelectric effect has many uses. One of those is that it allows scientists to probe the electron energy levels in matter by determining the threshold frequency at which incident light causes emission. Photomultiplier tubes making use of this effect were also used in older television cameras.

A very useful application of the photoelectric effect is in the construction of solar panels. Solar panels are arrays of photovoltaic cells, which are cells that make use of electrons ejected from metals by solar radiation to generate current. As of 2018, nearly 3 percent of the world’s energy is generated by solar panels, but this number is expected to grow considerably over the next several years, especially as the efficiency of such panels increases.

But most important of all, the discovery and understanding of the photoelectric effect laid the groundwork for the field of quantum mechanics and a better understanding of the nature of light.

Photoelectric Effect Experiments

There are many experiments that can be performed in an introductory physics lab to demonstrate the photoelectric effect. Some of these are more complicated than others.

A simple experiment demonstrates the photoelectric effect with an electroscope and a UV-C lamp providing ultraviolet light. Place negative charge on the electroscope so that the needle deflects. Then, shine the UV-C lamp. Light from the lamp will release electrons from the electroscope and discharge it. You can tell this happens by seeing the needle’s deflection reducing. Note, however, that if you tried the same experiment with a positively charged electroscope, it wouldn’t work.

There are many other possible ways to experiment with the photoelectric effect. Several setups involve a photocell consisting of a large anode that, when hit with incident light, will release electrons that are picked up by a cathode. If this setup is connected to a voltmeter, for example, the photoelectric effect will become apparent when shining the light creates a voltage.

More complex setups allow for more accurate measurement and even allow you to determine the work function and threshold frequencies for different materials. See the Resources section for links.

Related Articles

• Physics Hypertextbook: Photoelectric Effect
• Georgia State University: HyperPhysics: Photoelectric Effect
• UTK: Lab 2: The Photoelectric Effect
• UCLA Physics and Astronomy: Experiment 6 – The Photoelectric Effect
• Amrita: Photoelectric Effect

About the Author

Gayle Towell is a freelance writer and editor living in Oregon. She earned masters degrees in both mathematics and physics from the University of Oregon after completing a double major at Smith College, and has spent over a decade teaching these subjects to college students. Also a prolific writer of fiction, and founder of Microfiction Monday Magazine, you can learn more about Gayle at gtowell.com.

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1.3: Photoelectric Effect Explained with Quantum Hypothesis

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Learning Objectives

• To be familiar with the photoelectron effect for bulk materials
• Understand how the photoelectron kinetic energy and intensity vary as a function of incident light wavelength
• Understand how the photoelectron kinetic energy and intensity vary as a function of incident light intensity
• Describe what a workfunction is and relate it to ionization energy
• Describe the photoelectric effect with Einstein's quantized photon model of light

Nature, it seemed, was quantized (non-continuous, or discrete). If this was so, how could Maxwell’s equations correctly predict the result of the blackbody radiator? Planck spent a good deal of time attempting to reconcile the behavior of electromagnetic waves with the discrete nature of the blackbody radiation, to no avail. It was not until 1905, with yet another paper published by Albert Einstein, that the wave nature of light was expanded to include the particle interpretation of light which adequately explained Planck’s equation.

The photoelectric effect was first documented in 1887 by the German physicist Heinrich Hertz and is therefore sometimes referred to as the Hertz effect. While working with a spark-gap transmitter (a primitive radio-broadcasting device), Hertz discovered that upon absorption of certain frequencies of light, substances would give off a visible spark. In 1899, this spark was identified as light-excited electrons (called photoelectrons ) leaving the metal's surface by J.J. Thomson (Figure 1.3.1 ).

The classical picture underlying the photoelectron effect was that the atoms in the metal contained electrons, that were shaken and caused to vibrate by the oscillating electric field of the incident radiation. Eventually some of them would be shaken loose, and would be ejected from the cathode. It is worthwhile considering carefully how the number and speed of electrons emitted would be expected to vary with the intensity and color of the incident radiation along with the time needed to observe the photoelectrons.

• Increasing the intensity of radiation would shake the electrons more violently, so one would expect more to be emitted, and they would shoot out at greater speed, on average.
• Increasing the frequency of the radiation would shake the electrons faster, so it might cause the electrons to come out faster. For very dim light, it would take some time for an electron to work up to a sufficient amplitude of vibration to shake loose.

Lenard's Experimental Results (Intensity Dependence)

In 1902, Hertz's student, Philipp Lenard, studied how the energy of the emitted photoelectrons varied with the intensity of the light. He used a carbon arc light and could increase the intensity a thousand-fold. The ejected electrons hit another metal plate, the collector, which was connected to the cathode by a wire with a sensitive ammeter, to measure the current produced by the illumination (Figure 1.3.2 ). To measure the energy of the ejected electrons, Lenard charged the collector plate negatively, to repel the electrons coming towards it. Thus, only electrons ejected with enough kinetic energy to get up this potential hill would contribute to the current.

Lenard discovered that there was a well defined minimum voltage that stopped any electrons getting through (\(V_{stop}\)). To Lenard's surprise, he found that \(V_{stop}\) did not depend at all on the intensity of the light! Doubling the light intensity doubled the number of electrons emitted, but did not affect the kinetic energies of the emitted electrons. The more powerful oscillating field ejected more electrons, but the maximum individual energy of the ejected electrons was the same as for the weaker field (Figure 1.3.2 ).

Millikan's Experimental Results (Wavelength Dependence)

The American experimental physicist Robert Millikan followed up on Lenard's experiments and using a powerful arc lamp, he was able to generate sufficient light intensity to separate out the colors and check the photoelectric effect using light of different colors. He found that the maximum energy of the ejected electrons did depend on the color - the shorter wavelength, higher frequency light eject photoelectrons with greater kinetic energy (Figures 1.3.3 ).

As shown in Figure 1.3.4 , just the opposite behavior from classical is observed from Lenard's and Millikan's experiments. The intensity affects the number of electrons, and the frequency affects the kinetic energy of the emitted electrons. From these sketches, we see that

• the kinetic energy of the electrons is linearly proportional to the frequency of the incident radiation above a threshold value of \(ν_0\) (no current is observed below \(ν_0\)), and the kinetic energy is independent of the intensity of the radiation, and
• the number of electrons (i.e. the electric current) is proportional to the intensity and independent of the frequency of the incident radiation above the threshold value of \(ν_0\) (i.e., no current is observed below \(ν_0\)).

Classical Theory does not Describe Experiment

Classical theory predicts that energy carried by light is proportional to its amplitude independent of its frequency, and this fails to correctly explain the observed wavelength dependence in Lenard's and Millikan's observations.

As with most of the experimental results we discuss in this text, the behavior described above is a simplification of the true experimental results observed in the laboratory. A more complex description involves a greater introduction of more complex physics and instrumentation, which will be ignored for now.

Einstein's Quantum Picture

In 1905 Einstein gave a very simple interpretation of Lenard's results and borrowed Planck's hypothesis about the quantized energy from his blackbody research and assumed that the incoming radiation should be thought of as quanta of energy \(h\nu\), with \(\nu\) the frequency. In photoemission, one such quantum is absorbed by one electron. If the electron is some distance into the material of the cathode, some energy will be lost as it moves towards the surface. There will always be some electrostatic cost as the electron leaves the surface, which is the workfunction, \(\Phi\). The most energetic electrons emitted will be those very close to the surface, and they will leave the cathode with kinetic energy

\[KE = h\nu - \Phi \label{Eq1} \]

On cranking up the negative voltage on the collector plate until the current just stops, that is, to \(V_{stop}\), the highest kinetic energy electrons (\(KE_e\)) must have had energy \(eV_{stop}\) upon leaving the cathode. Thus,

\[eV_{stop} = h\nu - \Phi \label{Eq2} \]

Thus, Einstein's theory makes a very definite quantitative prediction: if the frequency of the incident light is varied, and \(V_{stop}\) plotted as a function of frequency, the slope of the line should be \(\frac{h}{e}\) (Figure \(\PageIndex{4A}\)). It is also clear that there is a minimum light frequency for a given metal \(\nu_o\), that for which the quantum of energy is equal to \(\Phi\) (Equation \ref{Eq1}). Light below that frequency, no matter how bright, will not eject electrons.

According to both Planck and Einstein, the energy of light is proportional to its frequency rather than its amplitude, there will be a minimum frequency \(\nu_0\) needed to eject an electron with no residual energy.

Since every photon of sufficient energy excites only one electron, increasing the light's intensity (i.e. the number of photons/sec) only increases the number of released electrons and not their kinetic energy. In addition, no time is necessary for the atom to be heated to a critical temperature and therefore the release of the electron is nearly instantaneous upon absorption of the light. Finally, because the photons must be above a certain energy to satisfy the workfunction, a threshold frequency exists below which no photoelectrons are observed. This frequency is measured in units of Hertz (1/second) in honor of the discoverer of the photoelectric effect.

Einstein's Equation \(\ref{Eq1}\) explains the properties of the photoelectric effect quantitatively. A strange implication of this experiment is that light can behave as a kind of massless "particle" now known as a photon whose energy \(E=h\nu\) can be transferred to an actual particle (an electron), imparting kinetic energy to it, just as in an elastic collision between to massive particles such as billiard balls.

Robert Millikan initially did not accept Einstein's theory, which he saw as an attack on the wave theory of light, and worked for ten years until 1916, on the photoelectric effect. He even devised techniques for scraping clean the metal surfaces inside the vacuum tube. For all his efforts he found disappointing results: he confirmed Einstein's theory after ten years. In what he writes in his paper, Millikan is still desperately struggling to avoid this conclusion. However, by the time of his Nobel Prize acceptance speech, he has changed his mind rather drastically!

Einstein's simple explanation (Equation \ref{Eq1}) completely accounted for the observed phenomena in Lenard's and Millikan's experiments (Figure 1.3.4 ) and began an investigation into the field we now call quantum mechanics . This new field seeks to provide a quantum explanation for classical mechanics and create a more unified theory of physics and thermodynamics. The study of the photoelectric effect has also lead to the creation of new field of photoelectron spectroscopy. Einstein's theory of the photoelectron presented a completely different way to measure Planck's constant than from black-body radiation.

The Workfunction (Φ)

The workfunction is an intrinsic property of the metal. While the workfunctions and ionization energies appear as similar concepts, they are independent. The workfunction of a metal is the minimum amount of energy (\(\ce{E}\)) necessary to remove an electron from the surface of the bulk ( solid ) metal (sometimes referred to as binding energy ).

\[\ce{M (s) + \Phi \rightarrow M^{+}(s) + e^{-}}(\text{free with no kinetic energy}) \nonumber \]

The workfunction is qualitatively similar to ionization energy (\(\ce{IE}\)), which is the amount of energy required to remove an electron from an atom or molecule in the gaseous state.

\[\ce{M (g) + IE \rightarrow M^{+}(g) + e^{-}} (\text{free with no kinetic energy}) \nonumber \]

However, these two energies differ in magnitude (Table 1.3.1 ). For instance, copper has a workfunction of about 4.7 eV, but has a higher ionization energy of 7.7 eV. Generally, the ionization energies for metals are greater than the corresponding workfunctions (i.e., the electrons are less tightly bound in bulk metal).

Example 1.3.1 : Calcium

• What is the energy in joules and electron volts of a photon of 420-nm violet light?
• What is the maximum kinetic energy of electrons ejected from calcium by 420-nm violet light, given that the workfunction for calcium metal is 2.71 eV?

To solve part (a), note that the energy of a photon is given by \(E=h\nu\). For part (b), once the energy of the photon is calculated, it is a straightforward application of Equation \ref{Eq1} to find the ejected electron’s maximum kinetic energy, since \(\Phi\) is given.

Solution for (a)

Photon energy is given by

\[E = h\nu \nonumber \]

Since we are given the wavelength rather than the frequency, we solve the familiar relationship \(c=\nu\lambda\) for the frequency, yielding

\[\nu=\dfrac{c}{\lambda} \nonumber \]

Combining these two equations gives the useful relationship

\[E=\dfrac{hc}{\lambda} \nonumber \]

Now substituting known values yields

\[\begin{align*} E &= \dfrac{(6.63 \times 10^{-34}\; J \cdot s)(3.00 \times 10^8 m/s)}{420 \times 10^{-9}\; m} \\[4pt] &= 4.74 \times 10^{-19}\; J \end{align*} \nonumber \]

Converting to eV, the energy of the photon is

\[\begin{align*} E&=(4.74 \times 10^{-19}\; J) \left( \dfrac{1 \;eV}{1.6 \times 10^{-19}\;J} \right) \\[4pt] &= 2.96\; eV. \nonumber \end{align*} \nonumber \]

Solution for (b)

Finding the kinetic energy of the ejected electron is now a simple application of Equation \ref{Eq1}. Substituting the photon energy and binding energy yields

\[\begin{align*} KE_e &=h\nu – \Phi \\[4pt] &= 2.96 \;eV – 2.71 \;eV \\[4pt] &= 0.246\; eV.\nonumber \end{align*} \nonumber \]

The energy of this 420-nm photon of violet light is a tiny fraction of a joule, and so it is no wonder that a single photon would be difficult for us to sense directly—humans are more attuned to energies on the order of joules. But looking at the energy in electron volts, we can see that this photon has enough energy to affect atoms and molecules. A DNA molecule can be broken with about 1 eV of energy, for example, and typical atomic and molecular energies are on the order of eV, so that the UV photon in this example could have biological effects.

The ejected electron (called a photoelectron) has a rather low energy, and it would not travel far, except in a vacuum. The electron would be stopped by a retarding potential of 0.26 eV. In fact, if the photon wavelength were longer and its energy less than 2.71 eV, then the formula would give a negative kinetic energy, an impossibility. This simply means that the 420-nm photons with their 2.96-eV energy are not much above the frequency threshold. You can show for yourself that the threshold wavelength is 459 nm (blue light). This means that if calcium metal is used in a light meter, the meter will be insensitive to wavelengths longer than those of blue light. Such a light meter would be insensitive to red light, for example.

Exercise 1.3.1 : Silver

What is the longest-wavelength electromagnetic radiation that can eject a photoelectron from silver? Is this in the visible range?

Given that the workfunction is 4.72 eV from Table 1.3.1 , then only photons with wavelengths lower than 263 nm will induce photoelectrons (calculated via \(E=h \nu\)). This is ultraviolet and not in the visible range.

Exercise 1.3.2

Why is the workfunction of an element generally lower than the ionization energy of that element?

The workfunction of a metal refers to the minimum energy required to extract an electron from the surface of a ( bulk ) metal by the absorption a photon of light. The workfunction will vary from metal to metal. In contrast, ionization energy is the energy needed to detach electrons from atoms and also varies with each particular atom, with the valence electrons require less energy to extract than core electrons (i.e., from lower shells) that are more closely bound to the nuclei. The electrons in the metal lattice there less bound (i.e., free to move within the metal) and removing one of these electrons is much easier than removing an electron from an atom because the metallic bonds of the bulk metal reduces their binding energy. As we will show in subsequent chapters, the more delocalized a particle is, the lower its energy.

Although Hertz discovered the photoelectron in 1887, it was not until 1905 that a theory was proposed that explained the effect completely. The theory was proposed by Einstein and it made the claim that electromagnetic radiation had to be thought of as a series of particles, called photons, which collide with the electrons on the surface and emit them. This theory ran contrary to the belief that electromagnetic radiation was a wave and thus it was not recognized as correct until 1916 when Robert Millikan experimentally confirmed the theory

The photoelectric effect is the process in which electromagnetic radiation ejects electrons from a material. Einstein proposed photons to be quanta of electromagnetic radiation having energy \(E=h\nu\) is the frequency of the radiation. All electromagnetic radiation is composed of photons. As Einstein explained, all characteristics of the photoelectric effect are due to the interaction of individual photons with individual electrons. The maximum kinetic energy \(KE_e\) of ejected electrons (photoelectrons) is given by \(KE_e=h\nu – \Phi\), where \(h\nu\) is the photon energy and \(\Phi\) is the workfunction (or binding energy) of the electron to the particular material.

Conceptual Questions

• Is visible light the only type of electromagnetic radiation that can cause the photoelectric effect?
• Which aspects of the photoelectric effect cannot be explained without photons? Which can be explained without photons? Are the latter inconsistent with the existence of photons?
• Is the photoelectric effect a direct consequence of the wave character of electromagnetic radiation or of the particle character of electromagnetic radiation? Explain briefly.
• Insulators (nonmetals) have a higher \(\Phi\) than metals, and it is more difficult for photons to eject electrons from insulators. Discuss how this relates to the free charges in metals that make them good conductors.
• If you pick up and shake a piece of metal that has electrons in it free to move as a current, no electrons fall out. Yet if you heat the metal, electrons can be boiled off. Explain both of these facts as they relate to the amount and distribution of energy involved with shaking the object as compared with heating it.

Contributors and Attributions

Michael Fowler  (Beams Professor,  Department of Physics ,  University of Virginia)

Mark Tuckerman ( New York University )

David M. Hanson, Erica Harvey, Robert Sweeney, Theresa Julia Zielinski (" Quantum States of Atoms and Molecules ")

Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors.  Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/[email protected] ).

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5.2: The Photoelectric Effect

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Light Interacting with Conductors

The common denominator of the problems that would plague physics for the early years of the 20th century involved light’s interaction with matter.  As the blackbody radiation puzzle showed, the simple view developed from Maxwell’s EM and Boltzmann’s thermodynamics, were not sufficient to handle these problems.  A whole new way of thinking about light and matter was needed.  Planck started the revolution (without thinking it was correct), and the next bit of evidence would come from a second 1905 paper by Einstein, explaining a phenomenon relating to light striking a conducting surface.

When we studied EM in Physics 9C, we always assumed that charges on the surfaces of conductors remained on those conductors.  But this belied the fact that we would sometimes see charges leap from a conducting surface (a spark) due to a strong external field.  So we know that given enough additional energy (in the case of the spark, electrical potential energy), an electron will exit the surface of a metal (the protons are of course fixed within the lattice of the metal).  Different metals will hold their electrons with differing degrees of “tightness,” and this tightness is measured in terms of the minimum amount of energy needed to just barely free the most loosely-held electrons.  This minimum energy for a given metal is called the metal’s work function , typically represented by the symbol \(\phi\).  Naturally an external static electric field is not the only way to give additional energy to these electrons, and it was known for quite some time that shining light on the metal can also add enough energy to the electrons to kick some off. When light accomplishes this, it is called the photoelectric effect .

At first glance, this phenomenon makes perfect sense – there is no sign of any of the "weirdness" that came out of Planck's explanation of the blackbody radiation curve a few years earlier. When light is shone onto the negative plate of a capacitor, some electrons are ejected and make their way to the positive plate. When the the missing electrons are replaced on the plate form the battery, the electron flow can be measured by an ammeter. If we turn up the brightness of the light, the measured current rises.

Figure 5.2.1 - Photoelectric Effect (Unsurprising)

Digging Deeper

Physics is uninteresting if we are never surprised, so let’s dig a little deeper and determine two other pieces of information, namely:

• Does this effect have any frequency dependence?
• What determines how much kinetic energy the electrons have after they exit the conductor?

So rather than just use white light, let’s compare some monochromatic cases.

Figure 5.2.2 - Frequency Dependence of Photoelectric Effect

The blue light ejects electrons even when dim, as the white light did, but dim red light does not.  This tells us that it was the blue part of the spectrum that was ejecting the electrons when the white light was shone on the metal earlier.  While this result is peculiar from our standard understanding of EM, we can simply look at it as a confirmation of Planck’s result from blackbody radiation: Blue light carries more energy than red light, since it is providing enough energy for the electrons to overcome the work function.  So in order to see the same effect with red light as we saw  with blue light, we just need to crank up the intensity of the red light to make up for the energy deficiency, right?  No, it turns out it doesn’t work this way at all!

Einstein explained the phenomenon in the following way: Notwithstanding light’s obvious wavelike nature, in this setting it behaves like a particle (which we now call a photon ), inasmuch as it can only be absorbed by a single electron, and only one photon strikes an electron at a time.  We can call this the “one per customer” rule.  This photon has an energy equal to \(hf\) (just as Planck found), and it gives all this energy to the electron it strikes.

Notice how perfectly this explains what we see.  Any given electron must receive an amount of energy greater than the work function in order to be set free, but the most it can receive is \(hf\), and if \(f\) is too low, then it won’t be enough.  The light doesn’t behave like a wave in this case, which could continuously and gradually add energy to the electron until it has enough, but rather like a particle, in an all-or-nothing fashion.  Furthermore, the intensity of the light is simply determined by the number of photons arriving per second.  If the photons have enough energy to kick off electrons, then greater intensity means more electrons will be kicked per second, but if the individual photons don’t have enough energy to kick off electrons, then adding more of them will not have any effect – they cannot "double-up" on an electron – there's only one per customer. Furthermore, a particularly energetic (high frequency) photon cannot split its energy between two electrons and eject them both.

This answers the effect of frequency, but what about the second "digging deeper" question regarding the energy of the electrons that are ejected?  Einstein’s solution gives us that answer as well.  Applying conservation of energy to this process gives us immediately what we seek:

Figure 5.2.3 - Photoelectric Effect Energy Accounting

From conservation of energy, we see immediately that of the energy introduced by the photon, some of it goes into the potential energy that is the work function of the metal (freeing the charge), and the remainder into the electron’s kinetic energy. It should be noted that the work function is not a constant that applies to every electron – some will be bound more tightly to the metal than others. The work function is defined as the  minimum  binding energy for that metal – the energy required to tear away the easiest-to-remove electrons. This work function is found by measured something called the  stopping potential , which works like this:

Figure 5.2.4 - Stopping Potential

Here we are shining onto the positively-charged plate, ejecting electrons. The electrons come off the plate with some kinetic energy, but the electric field opposes their motion. If the field between the plates is weak, then some electrons will get across, and we can measure the flow. As we dial-up the strength of the field, however, fewer and fewer of the electrons will successfully make the journey. When the field is just barely strong enough to stop even the most energetically-ejected particles, then the potential energy that those electrons have to climb equals the kinetic energy at which they were ejected. As monochromatic light was used, every electron was given the same energy, so those that are ejected with the most kinetic energy are the ones held most weakly to the conductor. This minimum potential energy of the conductor is what we define to be its work function. Mathematically, the energy accounting looks like this:

\[e\Delta V_{stopping}={KE}_{max}=hf - \phi\]

This equation is read this way: "The electron charge multiplied by the stopping (electrostatic) potential is the potential energy change that barely stops the electrons with the greatest amount of kinetic energy, and this equals the energy given to the electron by the photon, minus the work function (the potential energy holding the electron to the surface of the conductor)."

Applications

The applications of this effect are of course endless, as you can undoubtedly think of countless devices that involve detection of light. One interesting application is a device known as a photomultiplier tube . Suppose you wish to be able to detect and amplify very low intensities of light (in any part of the spectrum). Assuming you can find a metal with a low enough work function for the frequency of light you want to see, at low intensities the photons are only going to knock off a handful of electrons, which may not be particularly easy to detect. But the nice thing about converting a signal from photons to electrons is that we can add energy to electrons using electric fields, and electrons are also quite good (when propelled at sufficient KE ) at knocking more electrons off a surface. Then those can do the same, and so on.

This device is indispensable for high-energy particle physics experimentation, when it is important to see where even a single photon produced in a certain collision lands.  But it also works for common-use devices, such as night vision goggles.  In this case, you have lots of photons landing in different places (i.e. an image focused by a lens), and each place where the photon lands has its own tiny photomultiplier tube.  Each tube constitutes one pixel, so all the tubes put together form an amplified image.  This device is a step above an infrared sensing apparatus for applications that require better resolution of the image (we’ll see why this is later), though it is constructed specifically for the visible spectrum, so it can’t see through objects opaque to visible light, while some of those same objects may be (partly) transparent to infrared light.

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High school physics - NGSS

Course: high school physics - ngss   >   unit 6.

• Effects of different wavelengths of radiation

The photoelectric effect

• Understand: electromagnetic radiation and matter
• Apply: electromagnetic radiation and matter

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Video transcript

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Einstein and the photoelectric effect

Bohr’s theory of the atom, scattering of x-rays, de broglie’s wave hypothesis.

• Schrödinger’s wave mechanics
• Electron spin and antiparticles
• Identical particles and multielectron atoms
• Time-dependent Schrödinger equation
• Axiomatic approach
• Incompatible observables
• Heisenberg uncertainty principle
• Quantum electrodynamics
• The electron: wave or particle?
• Hidden variables
• Paradox of Einstein, Podolsky, and Rosen
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• Decay of the kaon
• Cesium clock
• A quantum voltage standard

• What is Richard Feynman famous for?
• What did Werner Heisenberg do during World War II?
• What is Werner Heisenberg best known for?
• How did Werner Heisenberg contribute to atomic theory?

Bohr’s theory was a brilliant step forward. Its two most important features have survived in present-day quantum mechanics. They are (1) the existence of stationary, nonradiating states and (2) the relationship of radiation frequency to the energy difference between the initial and final states in a transition. Prior to Bohr, physicists had thought that the radiation frequency would be the same as the electron’s frequency of rotation in an orbit.

Soon scientists were faced with the fact that another form of radiation, X-rays, also exhibits both wave and particle properties. Max von Laue of Germany had shown in 1912 that crystals can be used as three-dimensional diffraction gratings for X-rays; his technique constituted the fundamental evidence for the wavelike nature of X-rays. The atoms of a crystal, which are arranged in a regular lattice, scatter the X-rays. For certain directions of scattering, all the crests of the X-rays coincide. (The scattered X-rays are said to be in phase and to give constructive interference.) For these directions, the scattered X-ray beam is very intense. Clearly, this phenomenon demonstrates wave behaviour. In fact, given the interatomic distances in the crystal and the directions of constructive interference , the wavelength of the waves can be calculated.

Faced with evidence that electromagnetic radiation has both particle and wave characteristics, Louis-Victor de Broglie of France suggested a great unifying hypothesis in 1924. De Broglie proposed that matter has wave as well as particle properties. He suggested that material particles can behave as waves and that their wavelength λ is related to the linear momentum p of the particle by λ = h / p .

In 1927 Clinton Davisson and Lester Germer of the United States confirmed de Broglie’s hypothesis for electrons. Using a crystal of nickel, they diffracted a beam of monoenergetic electrons and showed that the wavelength of the waves is related to the momentum of the electrons by the de Broglie equation. Since Davisson and Germer’s investigation, similar experiments have been performed with atoms, molecules, neutrons, protons, and many other particles. All behave like waves with the same wavelength-momentum relationship.

Basic concepts and methods

Bohr’s theory, which assumed that electrons moved in circular orbits, was extended by the German physicist Arnold Sommerfeld and others to include elliptic orbits and other refinements. Attempts were made to apply the theory to more complicated systems than the hydrogen atom. However, the ad hoc mixture of classical and quantum ideas made the theory and calculations increasingly unsatisfactory. Then, in the 12 months started in July 1925, a period of creativity without parallel in the history of physics , there appeared a series of papers by German scientists that set the subject on a firm conceptual foundation. The papers took two approaches: (1) matrix mechanics, proposed by Werner Heisenberg , Max Born , and Pascual Jordan , and (2) wave mechanics , put forward by Erwin Schrödinger . The protagonists were not always polite to each other. Heisenberg found the physical ideas of Schrödinger’s theory “disgusting,” and Schrödinger was “discouraged and repelled” by the lack of visualization in Heisenberg’s method. However, Schrödinger, not allowing his emotions to interfere with his scientific endeavours, showed that, in spite of apparent dissimilarities, the two theories are equivalent mathematically. The present discussion follows Schrödinger’s wave mechanics because it is less abstract and easier to understand than Heisenberg’s matrix mechanics.

Photoelectric Effect: Explanation & Applications

The photoelectric effect refers to what happens when electrons are emitted from a material that has absorbed electromagnetic radiation. Physicist Albert Einstein was the first to describe the effect fully, and received a Nobel Prize for his work. 

What is the photoelectric effect?

Light with energy above a certain point can be used to knock electrons loose , freeing them from a solid metal surface, according to Scientific American. Each particle of light, called a photon, collides with an electron and uses some of its energy to dislodge the electron. The rest of the photon's energy transfers to the free negative charge, called a photoelectron.

Understanding how this works revolutionized modern physics. Applications of the photoelectric effect brought us "electric eye" door openers, light meters used in photography, solar panels and photostatic copying.

Before Einstein, the effect had been observed by scientists, but they were confused by the behavior because they didn't fully understand the nature of light. In the late 1800s, physicists James Clerk Maxwell in Scotland and Hendrik Lorentz in the Netherlands determined that light appears to behave as a wave. This was proven by seeing how light waves demonstrate interference, diffraction and scattering, which are common to all sorts of waves (including waves in water.)

So Einstein's argument in 1905 that light can also behave as sets of particles was revolutionary because it did not fit with the classical theory of electromagnetic radiation. Other scientists had postulated the theory before him, but Einstein was the first to fully elaborate on why the phenomenon occurred – and the implications.

For example, Heinrich Hertz of Germany was the first person to see the photoelectric effect , in 1887. He discovered that if he shone ultraviolet light onto metal electrodes, he lowered the voltage needed to make a spark move behind the electrodes, according to English astronomer David Darling. 

Then in 1899, in England, J.J. Thompson demonstrated that ultraviolet light hitting a metal surface caused the ejection of electrons. A quantitative measure of the photoelectric effect came in 1902, with work by Philipp Lenard (a former assistant to Hertz.) It was clear that light had electrical properties, but what was going on was unclear.

According to Einstein, light is made up of little packets, at first called quanta and later photons. How quanta behave under the photoelectric effect can be understood through a thought experiment. Imagine a marble circling in a well, which would be like a bound electron to an atom. When a photon comes in, it hits the marble (or electron), giving it enough energy to escape from the well. This explains the behavior of light striking metal surfaces.

While Einstein, then a young patent clerk in Switzerland, explained the phenomenon in 1905, it took 16 more years for the Nobel Prize to be awarded for his work. This came after American physicist Robert Millikan not only verified the work, but also found a relation between one of Einstein's constants and Planck's constant. The latter constant describes how particles and waves behave in the atomic world. 

Further early theoretical studies on the photoelectric effect were performed by Arthur Compton in 1922 (who showed that X-rays also could be treated as photons and earned the Nobel Prize in 1927), as well as Ralph Howard Fowler in 1931 (who looked at the relationship between metal temperatures and photoelectric currents.)

Applications

While the description of the photoelectric effect sounds highly theoretical, there are many practical applications of its work. Britannica describes a few:

Photoelectric cells were originally used to detect light, using a vacuum tube containing a cathode, to emit electrons, and an anode, to gather the resulting current. Today, these "phototubes" have advanced to semiconductor-based photodiodes that are used in applications such as solar cells and fiber optics telecommunications.

Photomultiplier tubes are a variation of the phototube, but they have several metal plates called dynodes. Electrons are released after light strikes the cathodes. The electrons then fall onto the first dynode, which releases more electrons that fall on the second dynode, then on to the third, fourth, and so forth. Each dynode amplifies the current; after about 10 dynodes, the current is strong enough for the photomultipliers to detect even single photons. Examples of this are used in spectroscopy (which breaks apart light into different wavelengths to learn more about the chemical compositions of star, for example), and computerized axial tomography (CAT) scans that examine the body.

Other applications of photodiodes and photomultipliers include:

• imaging technology, including (older) television camera tubes or image intensifiers;
• studying nuclear processes;
• chemically analyzing materials based on their emitted electrons;
• giving theoretical information about how electrons in atoms transition between different energy states.

But perhaps the most important application of the photoelectric effect was setting off the quantum revolution , according to

Scientific American. It led physicists to think about the nature of light and the structure of atoms in an entirely new way.

Additional resources

• Physics Hypertextbook: Photoelectric Effect
• Khan Academy: Photoelectric Effect

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The Photoelectric Effect

Hertz finds maxwell's waves: and something else.

The most dramatic prediction of Maxwell's theory of electromagnetism, published in 1865, was the existence of electromagnetic waves moving at the speed of light, and the conclusion that light itself was just such a wave. This challenged experimentalists to generate and detect electromagnetic radiation using some form of electrical apparatus. The first clearly successful attempt was by Heinrich Hertz in 1886. He used a high voltage induction coil to cause a spark discharge between two pieces of brass, to quote him, " Imagine a cylindrical brass body, 3 cm in diameter and 26 cm long, interrupted midway along its length by a spark gap whose poles on either side are formed by spheres of 2 cm radius ." The idea was that once a spark formed a conducting path between the two brass conductors, charge would rapidly oscillate back and forth, emitting electromagnetic radiation of a wavelength similar to the size of the conductors themselves.

To prove there really was radiation emitted, it had to be detected. Hertz used a piece of copper wire 1 mm thick bent into a circle of diameter 7.5 cm, with a small brass sphere on one end, and the other end of the wire was pointed, with the point near the sphere. He added a screw mechanism so that the point could be moved very close to the sphere in a controlled fashion. This "receiver" was designed so that current oscillating back and forth in the wire would have a natural period close to that of the "transmitter" described above. The presence of oscillating charge in the receiver would be signaled by a spark across the (tiny) gap between the point and the sphere (typically, this gap was hundredths of a millimeter). (It was suggested to Hertz that this spark gap could be replaced as a detector by a suitably prepared frog's leg, but that apparently didn't work.)

The experiment was very successful — Hertz was able to detect the radiation up to fifty feet away, and in a series of ingenious experiments established that the radiation was reflected and refracted as expected, and that it was polarized. The main problem — the limiting factor in detection — was being able to see the tiny spark in the receiver. In trying to improve the spark's visibility, he came upon something very mysterious. To quote from Hertz again (he called the transmitter spark A , the receiver B ): " I occasionally enclosed the spark B in a dark case so as to more easily make the observations; and in so doing I observed that the maximum spark-length became decidedly smaller in the case than it was before. On removing in succession the various parts of the case, it was seen that the only portion of it which exercised this prejudicial effect was that which screened the spark B from the spark A. The partition on that side exhibited this effect, not only when it was in the immediate neighborhood of the spark B, but also when it was interposed at greater distances from B between A and B. A phenomenon so remarkable called for closer investigation ."

Hertz then embarked on a very thorough investigation. He found that the small receiver spark was more vigorous if it was exposed to ultraviolet light from the transmitter spark. It took a long time to figure this out - he first checked for some kind of electromagnetic effect, but found a sheet of glass effectively shielded the spark. He then found a slab of quartz did not shield the spark, whereupon he used a quartz prism to break up the light from the big spark into its components, and discovered that the wavelength which made the little spark more powerful was beyond the visible, in the ultraviolet.

In 1887, Hertz concluded what must have been months of investigation: "… I confine myself at present to communicating the results obtained, without attempting any theory respecting the manner in which the observed phenomena are brought about ."

Hallwachs' Simpler Approach

The next year, 1888, another German physicist, Wilhelm Hallwachs, in Dresden, wrote:

" In a recent publication Hertz has described investigations on the dependence of the maximum length of an induction spark on the radiation received by it from another induction spark. He proved that the phenomenon observed is an action of the ultraviolet light. No further light on the nature of the phenomenon could be obtained, because of the complicated conditions of the research in which it appeared. I have endeavored to obtain related phenomena which would occur under simpler conditions, in order to make the explanation of the phenomena easier. Success was obtained by investigating the action of the electric light on electrically charged bodies ."

He then describes his very simple experiment: a clean circular plate of zinc was mounted on an insulating stand and attached by a wire to a gold leaf electroscope, which was then charged negatively. The electroscope lost its charge very slowly. However, if the zinc plate was exposed to ultraviolet light from an arc lamp, or from burning magnesium, charge leaked away quickly. If the plate was positively charged, there was no fast charge leakage. (We showed this as a lecture demo, using a UV lamp as source.)

Questions for the reader : Could it be that the ultraviolet light somehow spoiled the insulating properties of the stand the zinc plate was on? Could it be that electric or magnetic effects from the large current in the arc lamp somehow caused the charge leakage?

Although Hallwach's experiment certainly clarified the situation, he did not offer any theory of what was going on.

J.J. Thomson Identifies the Particles

In fact, the situation remained unclear until 1899, when Thomson established that the ultraviolet light caused electrons to be emitted, the same particles found in cathode rays. His method was to enclose the metallic surface to be exposed to radiation in a vacuum tube, in other words to make it the cathode in a cathode ray tube. The new feature was that electrons were to be ejected from the cathode by the radiation, rather than by the strong electric field used previously.

By this time, there was a plausible picture of what was going on. Atoms in the cathode contained electrons, which were shaken and caused to vibrate by the oscillating electric field of the incident radiation. Eventually some of them would be shaken loose, and would be ejected from the cathode. It is worthwhile considering carefully how the number and speed of electrons emitted would be expected to vary with the intensity and color of the incident radiation. Increasing the intensity of radiation would shake the electrons more violently, so one would expect more to be emitted, and they would shoot out at greater speed, on average. Increasing the frequency of the radiation would shake the electrons faster, so might cause the electrons to come out faster. For very dim light, it would take some time for an electron to work up to a sufficient amplitude of vibration to shake loose.

Lenard Finds Some Surprises

In 1902, Lenard studied how the energy of the emitted photoelectrons varied with the intensity of the light. He used a carbon arc light, and could increase the intensity a thousand-fold. The ejected electrons hit another metal plate, the collector, which was connected to the cathode by a wire with a sensitive ammeter, to measure the current produced by the illumination. To measure the energy of the ejected electrons, Lenard charged the collector plate negatively, to repel the electrons coming towards it. Thus, only electrons ejected with enough kinetic energy to get up this potential hill would contribute to the current. Lenard discovered that there was a well defined minimum voltage that stopped any electrons getting through, we'll call it V stop .  To his surprise, he found that V stop  did not depend at all on the intensity of the light!  Doubling the light intensity doubled the number of electrons emitted, but did not affect the energies of the emitted electrons. The more powerful oscillating field ejected more electrons, but the maximum individual energy of the ejected electrons was the same as for the weaker field.

But Lenard did something else. With his very powerful arc lamp, there was sufficient intensity to separate out the colors and check the photoelectric effect using light of different colors. He found that the maximum energy of the ejected electrons did depend on the color — the shorter wavelength, higher frequency light caused electrons to be ejected with more energy. This was, however, a fairly qualitative conclusion — the energy measurements were not very reproducible, because they were extremely sensitive to the condition of the surface, in particular its state of partial oxidation. In the best vacua available at that time, significant oxidation of a fresh surface took place in tens of minutes. (The details of the surface are crucial because the fastest electrons emitted are those from right at the surface, and their binding to the solid depends strongly on the nature of the surface — is it pure metal or a mixture of metal and oxygen atoms?)

Question: In the above figure, the battery represents the potential Lenard used to charge the collector plate negatively, which would actually be a variable voltage source. Since the electrons ejected by the blue light are getting to the collector plate, evidently the potential supplied by the battery is less than V stop  for blue light. Show with an arrow on the wire the direction of the electric current in the wire.

Einstein Suggests an Explanation

In 1905 Einstein gave a very simple interpretation of Lenard's results.  He just assumed that the incoming radiation should be thought of as quanta of frequency  h f , with f the frequency. In photoemission, one such quantum is absorbed by one electron. The most energetic electrons emitted are found to have energy E depending on the light frequency as

E = h f − W ,  

where  W is a material-dependent constant.

It’s worth thinking carefully about  W . The standard explanation in many textbooks (and earlier versions of this lecture!) was that  W is the minimum work needed to tear the electron out of the emitter in the first place: the  work function  (hence  W ) of the emitter.  But this is wrong!  The voltage  V provided by the battery, or, more realistically, by some variable voltage source, is the voltage difference between  inside the metal  of the emitter and  inside the metal  of the collector.  The photon must provide sufficient energy to the electron to get it from inside the metal of the emitter to a point just  outside  the surface of the collector. But such a point is at a voltage the  collector  work function  W coll higher than that inside the metal of the collector! Therefore, the photon must deliver energy

h f = V + W coll ,  

where, remember,  V is the voltage provided by the battery (or other source of emf).

On cranking up the negative voltage until the current just stops, that is, to  V stop , the photon frequency is given by

e V stop = h f − W coll .  

Thus Einstein's theory makes a very definite quantitative prediction: if the frequency of the incident light is varied, and  V stop plotted as a function of frequency, the slope of the line should be  h / e .

It is also clear that there is a minimum light frequency for a given metal, that for which the quantum of energy is equal to the work function. Light below that frequency, no matter how bright, will not cause photoemission.

Millikan's Attempts to Disprove Einstein's Theory

If we accept Einstein's theory, then, this is a completely different way to measure Planck's constant. The American experimental physicist Robert Millikan , who did not accept Einstein's theory, which he saw as an attack on the wave theory of light, worked for ten years, until 1916, on the photoelectric effect. He even devised techniques for scraping clean the metal surfaces inside the vacuum tube. For all his efforts he found disappointing results: he confirmed Einstein's theory, measuring Planck's constant to within 0.5% by this method. One consolation was that he did get a Nobel prize for this series of experiments.

' Subtle is the Lord...' The Science and Life of Albert Einstein , Abraham Pais, Oxford 1982.

Inward Bound , Abraham Pais, Oxford, 1986

The Project Physics Course, Text , Holt, Rinehart, Winston, 1970

Life of Lenard

Life of Millikan

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• IIT JEE Study Material

Photoelectric Effect

The photoelectric effect is a phenomenon in which electrons are ejected from the surface of a metal when light is incident on it. These ejected electrons are called  photoelectrons . It is important to note that the emission of photoelectrons and the kinetic energy of the ejected photoelectrons is dependent on the frequency of the light that is incident on the metal’s surface. The process through which photoelectrons are ejected from the surface of the metal due to the action of light is commonly referred to as  photoemission .

Download Complete Chapter Notes of Structure of Atom Download Now

The photoelectric effect occurs because the electrons at the surface of the metal tend to absorb energy from the incident light and use it to overcome the attractive forces that bind them to the metallic nuclei. An illustration detailing the emission of photoelectrons as a result of the photoelectric effect is provided below.

History of the Photoelectric Effect Principle Formula Laws Governing the Photoelectric Effect Experimental Study of the Photoelectric Effect Einstien’s Photoelectric Equation Graphs Applications Solved Problems (Numericals)

Recommended Video

Photoelectric effect – basics.

Hertz and Lenard’s Observation

History of the Photoelectric Effect

The photoelectric effect was first introduced by Wilhelm Ludwig Franz Hallwachs in the year 1887, and the experimental verification was done by Heinrich Rudolf Hertz. They observed that when a surface is exposed to electromagnetic radiation at a higher threshold frequency, the radiation is absorbed, and the electrons are emitted. Today, we study the photoelectric effect as a phenomenon that involves a material absorbing electromagnetic radiation and releasing electrically charged particles.

To be more precise, light incident on the surface of a metal in the photoelectric effect causes electrons to be ejected. The electron ejected due to the photoelectric effect is called a photoelectron and is denoted by e – .  The current produced as a result of the ejected electrons is called photoelectric current.

Explaining the Photoelectric Effect: The Concept of Photons

The photoelectric effect cannot be explained by considering light as a wave. However, this phenomenon can be explained by the particle nature of light, in which light can be visualised as a stream of particles of electromagnetic energy. These ‘particles’ of light are called photons . The energy held by a photon is related to the frequency of the light via Planck’s equation .

E = h𝜈 = hc/λ

• E denotes the energy of the photon
• h is Planck’s constant
• 𝜈 denotes the frequency of the light
• c is the speed of light (in a vacuum)
• λ is the wavelength of the light

Thus, it can be understood that different frequencies of light carry photons of varying energies. For example, the frequency of blue light is greater than that of red light (the wavelength of blue light is much shorter than the wavelength of red light). Therefore, the energy held by a photon of blue light will be greater than the energy held by a photon of red light.

Threshold Energy for the Photoelectric Effect

For the photoelectric effect to occur, the photons that are incident on the surface of the metal must carry sufficient energy to overcome the attractive forces that bind the electrons to the nuclei of the metals. The minimum amount of energy required to remove an electron from the metal is called the  threshold energy  (denoted by the symbol Φ). For a photon to possess energy equal to the threshold energy, its frequency must be equal to the  threshold frequency  (which is the minimum frequency of light required for the photoelectric effect to occur). The threshold frequency is usually denoted by the symbol 𝜈 th , and the associated wavelength (called the threshold wavelength) is denoted by the symbol λ th . The relationship between the threshold energy and the threshold frequency can be expressed as follows.

Φ = h𝜈 th  = hc/λ th

Relationship between the Frequency of the Incident Photon and the Kinetic Energy of the Emitted Photoelectron

Therefore, the relationship between the energy of the photon and the kinetic energy of the emitted photoelectron can be written as follows:

E photon  = Φ + E electron

⇒  h𝜈 = h𝜈 th  + ½m e v 2

• E photon  denotes the energy of the incident photon, which is equal to h𝜈
• Φ denotes the threshold energy of the metal surface, which is equal to h𝜈 th
• E electron  denotes the kinetic energy of the photoelectron, which is equal to ½m e v 2  (m e = Mass of electron = 9.1*10 -31  kg)

If the energy of the photon is less than the threshold energy, there will be no emission of photoelectrons (since the attractive forces between the nuclei and the electrons cannot be overcome). Thus, the photoelectric effect will not occur if 𝜈 < 𝜈 th . If the frequency of the photon is exactly equal to the threshold frequency (𝜈 = 𝜈 th ), there will be an emission of photoelectrons, but their kinetic energy will be equal to zero. An illustration detailing the effect of the frequency of the incident light on the kinetic energy of the photoelectron is provided below.

From the image, it can be observed that

• The photoelectric effect does not occur when the red light strikes the metallic surface because the frequency of red light is lower than the threshold frequency of the metal.
• The photoelectric effect occurs when green light strikes the metallic surface, and photoelectrons are emitted.
• The photoelectric effect also occurs when blue light strikes the metallic surface. However, the kinetic energies of the emitted photoelectrons are much higher for blue light than for green light. This is because blue light has a greater frequency than green light.

It is important to note that the threshold energy varies from metal to metal. This is because the attractive forces that bind the electrons to the metal are different for different metals. It can also be noted that the photoelectric effect can also take place in non-metals, but the threshold frequencies of non-metallic substances are usually very high.

Einstein’s Contributions towards the Photoelectric Effect

The photoelectric effect is the process that involves the ejection or release of electrons from the surface of materials (generally a metal) when light falls on them. The photoelectric effect is an important concept that enables us to clearly understand the quantum nature of light and electrons.

After continuous research in this field, the explanation for the photoelectric effect was successfully explained by Albert Einstein. He concluded that this effect occurred as a result of light energy being carried in discrete quantised packets. For this excellent work, he was honoured with the Nobel Prize in 1921.

According to Einstein, each photon of energy E is

Where E = Energy of the photon in joule

h = Plank’s constant (6.626 × 10 -34 J.s)

ν = Frequency of photon in Hz

Properties of the Photon

• For a photon, all the quantum numbers are zero.
• A photon does not have any mass or charge, and they are not reflected in a magnetic and electric field.
• The photon moves at the speed of light in empty space.
• During the interaction of matter with radiation, radiation behaves as it is made up of small particles called photons.
• Photons are virtual particles. The photon energy is directly proportional to its frequency and inversely proportional to its wavelength.
• The momentum and energy of the photons are related, as given below

E = p.c where

p = Magnitude of the momentum

c = Speed of light

Definition of the Photoelectric Effect

Principle of the photoelectric effect.

The law of conservation of energy forms the basis for the photoelectric effect.

Minimum Condition for Photoelectric Effect

Threshold frequency (γ th ).

It is the minimum frequency of the incident light or radiation that will produce a photoelectric effect, i.e., the ejection of photoelectrons from a metal surface is known as the threshold frequency for the metal. It is constant for a specific metal but may be different for different metals.

If γ = Frequency of the incident photon and γ th = Threshold frequency, then,

• If γ < γ Th , there will be no ejection of photoelectron and, therefore, no photoelectric effect.
• If γ = γ Th , photoelectrons are just ejected from the metal surface; in this case, the kinetic energy of the electron is zero.
• If γ > γ Th , then photoelectrons will come out of the surface, along with kinetic energy.

Threshold Wavelength (λ th )

During the emission of electrons, a metal surface corresponding to the greatest wavelength to incident light is known as threshold wavelength.

λ th  = c/γ th

For wavelengths above this threshold, there will be no photoelectron emission. For λ = wavelength of the incident photon, then

• If λ < λ Th , then the photoelectric effect will take place, and ejected electron will possess kinetic energy.
• If λ = λ Th, then just the photoelectric effect will take place, and the kinetic energy of ejected photoelectron will be zero.
• If λ > λ Th, there will be no photoelectric effect.

Work Function or Threshold Energy (Φ)

The minimal energy of thermodynamic work that is needed to remove an electron from a conductor to a point in the vacuum immediately outside the surface of the conductor is known as work function/threshold energy.

Φ = hγ th  = hc/λ th

The work function is the characteristic of a given metal. If E = energy of an incident photon, then

• If E < Φ, no photoelectric effect will take place.
• If E = Φ, just a photoelectric effect will take place, but the kinetic energy of ejected photoelectron will be zero
• If E > photoelectron will be zero
• If E > Φ, the photoelectric effect will take place along with the possession of the kinetic energy by the ejected electron.

Photoelectric Effect Formula

According to  Einstein’s explanation of the photoelectric effect ,

The energy of photon = Energy needed to remove an electron + Kinetic energy of the emitted electron

i.e., hν = W + E

• ν is the frequency of the incident photon
• W is a work function
• E is the maximum kinetic energy of ejected electrons: 1/2 mv²

Laws Governing the Photoelectric Effect

• For a light of any given frequency,; (γ > γ Th ), the photoelectric current is directly proportional to the intensity of light.
• For any given material, there is a certain minimum (energy) frequency, called threshold frequency, below which the emission of photoelectrons stops completely, no matter how high the intensity of incident light is.
• The maximum kinetic energy of the photoelectrons is found to increase with the increase in the frequency of incident light, provided the frequency (γ > γ Th ) exceeds the threshold limit. The maximum kinetic energy is independent of the intensity of light.
• The photo-emission is an instantaneous process.

Experimental Study of the Photoelectric Effect

Photoelectric Effect: Experimental Setup

The given experiment is used to study the photoelectric effect experimentally. In an evacuated glass tube, two zinc plates, C and D, are enclosed. Plates C acts as an anode, and D acts as a photosensitive plate.

Two plates are connected to battery B and ammeter A. If the radiation is incident on plate D through a quartz window, W electrons are ejected out of the plate, and current flows in the circuit. This is known as photocurrent. Plate C can be maintained at desired potential (+ve or – ve) with respect to plate D.

Characteristics of the Photoelectric Effect

• The threshold frequency varies with the material, it is different for different materials.
• The photoelectric current is directly proportional to the light intensity.
• The kinetic energy of the photoelectrons is directly proportional to the light frequency.
• The stopping potential is directly proportional to the frequency, and the process is instantaneous.

Factors Affecting the Photoelectric Effect

With the help of this apparatus, we will now study the dependence of the photoelectric effect on the following factors:

• The intensity of incident radiation.
• A potential difference between the metal plate and collector.
• Frequency of incident radiation.

Effects of Intensity of Incident Radiation on Photoelectric Effect

The potential difference between the metal plate, collector and frequency of incident light is kept constant, and the intensity of light is varied.

The electrode C, i.e., the collecting electrode, is made positive with respect to D (metal plate). For a fixed value of frequency and the potential between the metal plate and collector, the photoelectric current is noted in accordance with the intensity of incident radiation.

It shows that photoelectric current and intensity of incident radiation both are proportional to each other. The photoelectric current gives an account of the number of photoelectrons ejected per sec.

Effects of Potential Difference between the Metal Plate and the Collector on the Photoelectric Effect

The frequency of incident light and intensity is kept constant, and the potential difference between the plates is varied.

Keeping the intensity and frequency of light constant, the positive potential of C is increased gradually. Photoelectric current increases when there is a positive increase in the potential between the metal plate and the collector up to a characteristic value.

There is no change in photoelectric current when the potential is increased higher than the characteristic value for any increase in the accelerating voltage. This maximum value of the current is called saturation current.

Effect of Frequency on Photoelectric Effect

The intensity of light is kept constant, and the frequency of light is varied.

For a fixed intensity of incident light, variation in the frequency of incident light produces a linear variation of the cut-off potential/stopping potential of the metal. It is shown that the cut-off potential (Vc) is linearly proportional to the frequency of incident light.

The kinetic energy of the photoelectrons increases directly proportionally to the frequency of incident light to completely stop the photoelectrons. We should reverse and increase the potential between the metal plate and collector in (negative value) so the emitted photoelectron can’t reach the collector.

Einstein’s Photoelectric Equation

According to Einstein’s theory of the photoelectric effect, when a photon collides inelastically with electrons, the photon is absorbed completely or partially by the electrons. So if an electron in a metal absorbs a photon of energy, it uses the energy in the following ways.

Some energy Φ 0  is used in making the surface electron free from the metal. It is known as the work function of the material. Rest energy will appear as kinetic energy (K) of the emitted photoelectrons.

Einstein’s Photoelectric Equation Explains the Following Concepts

• The frequency of the incident light is directly proportional to the kinetic energy of the electrons, and the wavelengths of incident light are inversely proportional to the kinetic energy of the electrons.
• If γ = γ th or λ =λ th then v max = 0
• γ < γ th  or λ > λ th : There will be no emission of photoelectrons.
• The intensity of the radiation or incident light refers to the number of photons in the light beam. More intensity means more photons and vice-versa. Intensity has nothing to do with the energy of the photon. Therefore, the intensity of the radiation is increased, and the rate of emission increases, but there will be no change in the kinetic energy of electrons. With an increasing number of emitted electrons, the value of the photoelectric current increases.

Different Graphs of the Photoelectric Equation

• Photoelectric current vs Retarding potential for different voltages
• Photoelectric current vs Retarding potential for different intensities
• Electron current vs Light Intensity
• Stopping potential vs Frequency
• Electron current vs Light frequency
• Electron kinetic energy vs Light frequency

Applications of the Photoelectric Effect

• Used to generate electricity in solar panels. These panels contain metal combinations that allow electricity generation from a wide range of wavelengths.
• Motion and Position Sensors: In this case, a photoelectric material is placed in front of a UV or IR LED. When an object is placed in between the Light-emitting diode (LED) and sensor, light is cut off, and the electronic circuit registers a change in potential difference
• Lighting sensors, such as the ones used in smartphones, enable automatic adjustment of screen brightness according to the lighting. This is because the amount of current generated via the photoelectric effect is dependent on the intensity of light hitting the sensor.
• Digital cameras can detect and record light because they have photoelectric sensors that respond to different colours of light.
• X-Ray Photoelectron Spectroscopy (XPS): This technique uses X-rays to irradiate a surface and measure the kinetic energies of the emitted electrons. Important aspects of the chemistry of a surface can be obtained, such as elemental composition, chemical composition, the empirical formula of compounds and chemical state.
• Photoelectric cells are used in burglar alarms.
• Used in photomultipliers to detect low levels of light.
• Used in video camera tubes in the early days of television.
• Night vision devices are based on this effect.
• The photoelectric effect also contributes to the study of certain nuclear processes. It takes part in the chemical analysis of materials since emitted electrons tend to carry specific energy that is characteristic of the atomic source.

Photoelectric Effect – JEE Advanced Concepts and Problems

Problems on the Photoelectric Effect

1. In a photoelectric effect experiment, the threshold wavelength of incident light is 260 nm and E (in eV) = 1237/λ (nm). Find the maximum kinetic energy of emitted electrons.

⇒ K max  = (1237) × [(380 – 260)/380×260] = 1.5 eV

Therefore, the maximum kinetic energy of emitted electrons in the photoelectric effect is 1.5 eV.

2. In a photoelectric experiment, the wavelength of the light incident on metal is changed from 300 nm to 400 nm and (hc/e = 1240 nm-V). Find the decrease in the stopping potential.

hc/λ 1  = ϕ + eV 1 . . . . (i)

hc/λ 2  = ϕ + eV 2 . . . . (ii)

Equation (i) – (ii)

hc(1/λ 1 – 1/λ 2 ) = e × (V 1 – V 2 )

= (1240 nm V) × 100nm/(300nm × 400nm)

=12.4/12 ≈ 1V

Therefore, the decrease in the stopping potential during the photoelectric experiment is 1V.

3. When ultraviolet light with a wavelength of 230 nm shines on a particular metal plate, electrons are emitted from plate 1, crossing the gap to plate 2 and causing a current to flow through the wire connecting the two plates. The battery voltage is gradually increased until the current in the ammeter drops to zero, at which point the battery voltage is 1.30 V. 

a) What is the energy of the photons in the beam of light in eV?

b) What is the maximum kinetic energy of the emitted electrons in eV?

Assuming that the wavelength corresponds to the wavelength in the vacuum.

f = 1.25 × 10 15 Hz

The energy of photon E = hf

E = (4.136 × 10 -15 )( 1.25 × 10 15)   

Note: Planck’s constant in eV s = 4.136 × 10 -15  eV s

E = 5.17 eV.

b) The maximum kinetic energy related to the emitted electron is stopping potential. In this case, the stopping potential is 1.30V. So the maximum kinetic energy of the electrons is 1.30V.

Also Check out:  JEE Main Photoelectric Effect Previous Year Questions with Solutions

Important Points to Remember

• If we consider the light with any given frequency, the photoelectric current is generally directly proportional to the intensity of light. However, the frequency should be above the threshold frequency in such a case.
• Below threshold frequency, the emission of photoelectrons completely stops despite the high intensity of incident light.
• A photoelectron’s maximum kinetic energy increases with an increase in the frequency of incident light. In this case, the frequency should exceed the threshold limit. Maximum kinetic energy is not affected by the intensity of light.
• Stopping potential is the negative potential of the opposite electrode when the photo-electric current falls to zero.
• The threshold frequency is described as the frequency when the photoelectric current stops below a particular frequency of incident light.
• The photoelectric effect establishes the quantum nature of radiation. This has been taken into account to be proof in favour of the particle nature of light.

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