millikan oil drop experiment theory

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Millikan oil-drop experiment

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• PhysicsLAB - Millikan's Oil Drop Experiment

Millikan oil-drop experiment , first direct and compelling measurement of the electric charge of a single electron . It was performed originally in 1909 by the American physicist Robert A. Millikan , who devised a straightforward method of measuring the minute electric charge that is present on many of the droplets in an oil mist. The force on any electric charge in an electric field is equal to the product of the charge and the electric field. Millikan was able to measure both the amount of electric force and magnitude of electric field on the tiny charge of an isolated oil droplet and from the data determine the magnitude of the charge itself.

Millikan’s original experiment or any modified version, such as the following, is called the oil-drop experiment. A closed chamber with transparent sides is fitted with two parallel metal plates, which acquire a positive or negative charge when an electric current is applied. At the start of the experiment, an atomizer sprays a fine mist of oil droplets into the upper portion of the chamber. Under the influence of gravity and air resistance, some of the oil droplets fall through a small hole cut in the top metal plate. When the space between the metal plates is ionized by radiation (e.g., X-rays ), electrons from the air attach themselves to the falling oil droplets, causing them to acquire a negative charge. A light source, set at right angles to a viewing microscope , illuminates the oil droplets and makes them appear as bright stars while they fall. The mass of a single charged droplet can be calculated by observing how fast it falls. By adjusting the potential difference, or voltage, between the metal plates, the speed of the droplet’s motion can be increased or decreased; when the amount of upward electric force equals the known downward gravitational force, the charged droplet remains stationary. The amount of voltage needed to suspend a droplet is used along with its mass to determine the overall electric charge on the droplet. Through repeated application of this method, the values of the electric charge on individual oil drops are always whole-number multiples of a lowest value—that value being the elementary electric charge itself (about 1.602 × 10 −19 coulomb). From the time of Millikan’s original experiment, this method offered convincing proof that electric charge exists in basic natural units. All subsequent distinct methods of measuring the basic unit of electric charge point to its having the same fundamental value.

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Milliken's Oil Drop Experiment

The Millikens Oil Drop Experiment was an experiment performed by Robert A. Millikan and Harvey Fletcher  in 1909 to measure the charge of an electron. This experiment proved to be very crucial in the physics community.

Millikens Oil Drop Experiment Definition

In the experiment, Milliken allowed charged tiny oil droplets to pass through a hole into an electric field. By varying the strength of the electric field the charge over an oil droplet was calculated, which always came as an integral value of ‘e.’

Apparatus of the Milliken’s Oil Drop Experiment

The apparatus for the experiment was constructed by Milliken and Fletcher. It incorporated two metal plates held at a distance by an insulated rod. There were four holes in the plate, out of which three were there to allow light to pass through them and one was there to allow viewing through the microscope.

Ordinary oil wasn’t used for the experiment as it would evaporate by the heat of the light and so could cause an error in the Millikens Oil Drop Experiment. So, the oil that is generally used in a vacuum apparatus which is of low vapour pressure was used.

Milliken’s Oil Drop Experiment Procedure

• Oil is passed through the atomizer from where it came in the form of tiny droplets. They pass the droplets through the holes present in the upper plate of the apparatus.
• The downward motions of droplets are observed through a microscope and the mass of oil droplets, then measure their terminal velocity.
• The air inside the chamber is ionized by passing a beam of X-rays through it. The electrical charge on these oil droplets is acquired by collisions with gaseous ions produced by ionization of air.
• The electric field is set up between the two plates and so the motion of charged oil droplets can be affected by the electric field.
• Gravity attracts the oil in a downward direction and the electric field pushes the charge upward. The strength of the electric field is regulated so that the oil droplet reaches an equilibrium position with gravity.
• The charge over the droplet is calculated at equilibrium, which is dependent on the strength of the electric field and mass of droplet.

Milliken’s Oil Drop Experiment Calculation

F up = F down

F up = Q . E

F down = m.g

Q  is  an  electron’s  charge,  E  is  the  electric  field,  m  is  the  droplet’s  mass,  and  g  is  gravity.

One can see how an electron charge is measured by Millikan. Millikan found that all drops had charges that were 1.6x 10 -19 C multiples.

Milliken’s Oil Drop Experiment Conclusion

The charge over any oil droplet is always an integral value of e (1.6 x 10 -19 ). Hence, the conclusion of  Millikens Oil Drop Experiment is that the charge is said to be quantized, i.e. the charge on any particle will always be an integral multiple of e.

Frequently Asked Questions – FAQs

What did millikan’s oil drop experiment measure.

Millikan oil-drop test, the first simple and persuasive electrical charge calculation of a single electron. It was first conducted by the American physicist Robert A. in 1909. He discovered that all the drops had charges that were simple multiples of a single integer, the electron’s fundamental charge.

What is the importance of Millikan’s oil drop experiment?

The experiment with Millikan is important since it defined the charge on an electron. Millikan used a very basic, very simple system in which the behaviour of gravitational, electrical, and (air) drag forces were controlled.

What did Millikan conclude after performing his oil drop experiment?

An integral multiple of the charge on an electron is the charge on every oil decrease. About an electric force. In a relatively small amount, the charge and mass of the atom must be condensed.

Why charges are quantized?

Charges are quantized since every object’s charge (ion, atom, etc.) Charge quantization, therefore, implies that no random values can be taken from the charge, but only values that are integral multiples of the fundamental charge (proton / electron charge).

Can charge be created or destroyed?

The Charge Conservation Law does not suggest that it is difficult to generate or remove electrical charges. It also means that any time a negative electrical charge is produced, it is important to produce an equal amount of positive electrical charge at the same time so that a system’s overall charge does not shift.

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The Millikan Oil Drop Experiment

Theresa Knott / Wikimedia Commons / CC BY-SA 3.0

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• Ph.D., Biomedical Sciences, University of Tennessee at Knoxville
• B.A., Physics and Mathematics, Hastings College

Robert Millikan's oil drop experiment measured the charge of the electron . The experiment was performed by spraying a mist of oil droplets into a chamber above the metal plates. The choice of oil was important because most oils would evaporate under the heat of the light source, causing the drop to change mass throughout the experiment. Oil for vacuum applications was a good choice because it had a very low vapor pressure. Oil droplets could become electrically charged through friction as they were sprayed through the nozzle or they could be charged by exposing them to ionizing radiation . Charged droplets would enter the space between the parallel plates. Controlling the electric potential across the plates would cause the droplets to rise or fall.

Calculations for the Experiment

F d = 6πrηv 1

where r is the drop radius, η is the viscosity of air and v 1 is the terminal velocity of the drop.

The weight W of the oil drop is the volume V multiplied by the density ρ and the acceleration due to gravity g.

The apparent weight of the drop in air is the true weight minus the upthrust (equal to the weight of air displaced by the oil drop). If the drop is assumed to be perfectly spherical then the apparent weight can be calculated:

W = 4/3 πr 3 g (ρ - ρ air )

The drop is not accelerating at terminal velocity so the total force acting on it must be zero such that F = W. Under this condition:

r 2 = 9ηv 1 / 2g(ρ - ρ air )

r is calculated so W can be solved. When the voltage is turned on the electric force on the drop is:

F E = qE

where q is the charge on the oil drop and E is the electric potential across the plates. For parallel plates:

E = V/d

where V is the voltage and d is the distance between the plates.

The charge on the drop is determined by increasing the voltage slightly so that the oil drop rises with velocity v 2 :

qE - W = 6πrηv 2

qE - W = Wv 2 /v 1

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Oil Drop Experiment

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Who Did the Oil Drop Experiment?

The Oil Drop Experiment was performed by the American physicist Robert A Millikan in 1909 to measure the electric charge carried by an electron . Their original experiment, or any modifications thereof to reach the same goal, are termed as oil drop experiments, in general.

What is the Oil Drop Experiment?

In the original version, Millikan and one of his graduate students, Harvey Fletcher, took a pair of parallel horizontal metallic plates. A uniform electric field was created in the intermediate space by applying a potential difference between them. The plates were held apart by a ring of insulating material. The ring had four holes, three for allowing light to illuminate the setup, and the fourth one enabled a microscope for viewing. A closed chamber with transparent walls was fitted above the plates.

At the beginning of the experiment, a fine mist of oil droplets was sprayed into the chamber. In modern setups, an atomizer replaces the oil droplets. The oil was so chosen such that it had a low vapor pressure and capable of charging. Some of the oil drops became electrically charged by friction as they forced their way out of the nozzle. Alternatively, charging could also be induced by incorporating a source of ionizing radiation , such as an X-Ray tube, in the apparatus. The droplets entered the space between the plates and raised or fell, according to the requirement, by varying plate voltage.

In terms of the present-day arrangement, when the electric field is turned off, the oil drops fall between the plates under the action of gravity only. The friction with the oil molecules in the chamber makes them reach their terminal velocity fast. The terminal velocity is the constant speed that a freely falling object eventually reaches when the resistance of the medium through which it is falling prevents further acceleration . Once the field is turned on, the charged drops start to rise. This motion happens since the electric force directed upwards is stronger than the gravitational force acting downwards. One charged drop is selected and kept at the center of the field of view of the microscope after allowing all other drops to fall by alternately switching off the voltage source. The experiment is conducted with this drop.

Theory and Calculations

First, the oil drop is allowed to fall in the absence of an electric field, and its terminal velocity, say v 1 , is found out. Using Stokes’ law, the drag force acting on the drop is calculated using the following formula.

Here r is the radius of the drop and ɳ, the viscosity of air.

The weight of the drop, w’, which is the product of its mass and acceleration due to gravity g, is given by the equation,

where ρ is the density of the oil.

However, what we need here is the apparent weight w of the drop in the air given by the difference of the actual weight and the upthrust of the air. We can express w  by the following formula.

Here ρ air denotes the density of air.

When the drop attains terminal velocity, then it has no acceleration. Hence, the total force acting on it must be zero. That means,

The above equation can be used to find out the value of r. Once r is calculated, the value of w can easily be found out from equation (i) marked above.

Now after turning on the electric field between the plates, the electric force F E acting on the drop is,

Where E is the electric field and q the charge on the oil drop. For parallel plates, the formula for E is,

Here V is the potential difference and d the distance between the plates. That implies,

Now if we adjust V to make the oil drop remain steady at a point, then

Thus, the value of q can be calculated.  By repeatedly applying this method to multiple oil droplets, the electric charge values on individual drops were always found to be integer multiples of the smallest value. This lowest charge could be nothing but the charge on the elementary particle, electron. By this method, the electronic charge was calculated to be approximate, 1.5924×10 −19  C, making an error of 1% of the currently accepted value, 1.602176487×10 −19 C. All subsequent research pointed to the same value of charge on the fundamental particle.

Millikan was able to measure both the amount of electric force and magnitude of electric field on the tiny charge of an isolated oil droplet and from the data determine the magnitude of the charge itself. Millikan’s oil drop experiment proved that the electric charge is quantized in nature. The electric charge appears in quanta of magnitude 1.6 X 10 -19 C in oil droplets.

Robert Millikan’s Oil Drop Experiment Animation

Millikan’s oil drop experiment and the atomic theory.

Until the time of the Oil Drop Experiment, the world had little or no knowledge of what is present inside an atom . Earlier experiments by the English Physicist J.J. Thomson had shown that atoms contain some negatively charged particles of masses significantly smaller than that of the hydrogen atom. Nevertheless, the exact value of the charge carried by these subatomic particles remained in the dark. The very existence of these particles was not accepted by many due to a lack of concrete evidence. Thus, the atomic model was shrouded in mystery. In this scenario, with Millikan’s groundbreaking effort to quantify the charge on an electron, the atomic theory came of age in the early years of the twentieth century.

Controversy about the Oil Drop Experiment and Discovery

Robert Millikan was the sole recipient of the Nobel Prize in Physics in 1923 for both his work in this classic experiment and his research in the photoelectric effect . Fletcher’s work on the oil drop project, however, was not recognized. Many years later, the writings of Fletcher revealed that Millikan wished to take the sole credit for the discovery in exchange for granting him a Ph.D. and helping him secure a job after his graduation.

The beauty of the oil drop experiment lies in its simple and elegant demonstration of the quantization of charge along with measuring the elementary charge on an electron that finds widespread applications to this day. With the progress of time, considerable modifications have been made to the original setup resulting in obvious perfection in the results. Still, no substantial deviation from the results of the classical experiment could yet be found.

• Robert Millikan and Harvey Fletcher conducted the oil drop experiment to determine the charge of an electron. The experiment was the first direct and riveting measurement of the electric charge of a single electron.
• They suspended tiny charged droplets of oil between two metal electrodes by balancing downward gravitational force with upward drag and electric forces.
• They later used their findings to determine the mass of the electron.
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Article was last reviewed on Thursday, February 2, 2023

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Millikan's Oil Drop Experiment: How to Determine the Charge of an Electron

• Author: Sam Brind

The Discovery of the Electron's Charge

In 1897, J. J. Thomson demonstrated that cathode rays, a new phenomenon, were made up of small, negatively charged particles, which were soon named electrons. The electron was the first subatomic particle ever discovered. Through his cathode ray experiments, Thomson also determined the electrical charge-to-mass ratio for the electron.

Millikan's oil-drop experiment was performed by Robert Millikan and Harvey Fletcher in 1909. It determined a precise value for the electric charge of the electron, e . The electron's charge is the fundamental unit of electric charge because all electric charges are made up of groups (or the absence of groups) of electrons. This discretisation of charge is also elegantly demonstrated by Millikan's experiment.

The unit of electric charge is a fundamental physical constant and crucial to calculations within electromagnetism. Hence, an accurate determination of its value was a big achievement, recognised by the 1923 Nobel Prize for Physics.

Robert Millikan, the 1923 Nobel prize winning physicist who determined the electron's charge.

Nobelprize.org

Millikan's Apparatus

Millikan's experiment is based on observing charged oil droplets in free fall and the presence of an electric field. A fine mist of oil is sprayed across the top of a perspex cylinder with a small 'chimney' that leads down to the cell (if the cell valve is open). The act of spraying will charge some of the released oil droplets through friction with the nozzle of the sprayer.

The cell is the area enclosed between two metal plates that are connected to a power supply. Hence, an electric field can be generated within the cell, and its strength can be varied by adjusting the power supply. A light is used to illuminate the cell, and the experimenter can observe the cell by looking through a microscope.

The apparatus used for Millikan's experiment (shown from two perspectives)

Terminal Velocity

As an object falls through a fluid, such as air or water, the force of gravity will accelerate the object and speed it up. As a consequence of this increasing speed, the drag force acting on the object that resists the falling also increases. Eventually, these forces will balance (along with a buoyancy force), and therefore the object no longer accelerates.

At this point, the object is falling at a constant speed, which is called the terminal velocity. The terminal velocity is the maximum speed the object will obtain while free-falling through the fluid.

Millikan's experiment revolves around the motion of individual charged oil droplets within the cell. To understand this motion, the forces acting on an individual oil droplet need to be considered. As the droplets are very small, they are reasonably assumed to be spherical in shape. The diagram below shows the forces and their directions that act on a droplet in two scenarios: when the droplet free falls and when an electric field causes the droplet to rise.

The different forces acting on a oil drop falling through air (left) and rising through air due to an applied electric field (right).

The most obvious force is the gravitational pull of the Earth on the droplet, also known as the weight of the droplet. Weight is given by the droplet volume multiplied by the density of the oil ( ρ oil ) multiplied by the gravitational acceleration ( g ). Earth's gravitational acceleration is known to be 9.81 m/s 2, and the density of the oil is usually also known (or could be determined in another experiment). However, the radius of the droplet ( r ) is unknown and extremely hard to measure.

As the droplet is immersed in the air (a fluid), it will experience an upward buoyancy force. Archimedes' principle states that this buoyancy force is equal to the weight of the fluid displaced by the submerged object.

Therefore, the buoyancy force acting on the droplet is an identical expression to the weight except that the density of air is used ( ρ air ). The density of air is a known value.

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The droplet also experiences a drag force that opposes its motion. This is also called air resistance and occurs as a consequence of friction between the droplet and the surrounding air molecules. Drag is described by Stoke's law, which says that the force depends on the droplet radius, the viscosity of air ( η ) and the velocity of the droplet ( v ). The viscosity of air is known, and the droplet velocity is unknown but can be measured.

When the droplet reaches its terminal velocity for falling ( v 1 ), the weight is equal to the buoyancy force plus the drag force. Substituting the previous equations for the forces and then rearranging gives an expression for the droplet radius. This allows the radius to be calculated if v 1 is measured.

When a voltage is applied to the brass plates, an electric field is generated within the cell. The strength of this electric field ( E ) is simply the voltage ( V ) divided by the distance separating the two plates ( d ).

If a droplet is charged, it will now experience an electrical force in addition to the three previously discussed forces. Negatively charged droplets will experience an upward force. This electrical force is proportional to both the electric field strength and the droplet's electrical charge ( q ).

If the electric field is strong enough, the negatively charged droplets will start to rise from a high enough voltage. When the droplet reaches its terminal velocity for rising ( v 2 ), the sum of the weight and drag is equal to the sum of the electrical force and the buoyancy force.

Equating the formulae for these forces, substituting in the previously obtained radius (from the fall of the same droplet), and rearranging gives an equation for the droplet's electrical charge. This means that the charge of a droplet can be determined through the measurement of the falling and rising terminal velocities, as the rest of the equation's terms are known constants.

Experimental Method

Firstly, calibration is performed, such as focusing the microscope and ensuring the cell is level. The cell valve is opened, oil is sprayed across the top of the cell, and the valve is then closed. Multiple droplets of oil will now be falling through the cell. The power supply is then turned on (to a sufficiently high voltage). This causes negatively charged droplets to rise but also makes positively charged droplets fall quicker, clearing them from the cell. After a very short time, this only leaves negatively charged droplets remaining in the cell.

The power supply is then turned off, and the drops begin to fall. A droplet is selected by the observer, who is watching through the microscope. Within the cell, a set distance has been marked, and the time for the selected droplet to fall through this distance is measured. These two values are used to calculate the falling terminal velocity. The power supply is then turned back on, and the droplet begins to rise.

The time to rise through the selected distance is measured and allows the rising terminal velocity to be calculated. This process could be repeated multiple times and allow average fall and rise times, and hence velocities, to be calculated. With the two terminal velocities obtained, the droplet's charge is calculated from the previous formula.

This method for calculating a droplet's charge was repeated for a large number of observed droplets. The charges were found to all be integer multiples ( n ) of a single number, a fundamental electric charge ( e ). Therefore, the experiment confirmed that the charge is quantised.

A value for e was calculated for each droplet by dividing the calculated droplet charge by an assigned value for n . These values were then averaged to give a final measurement of e .

Millikan obtained a value of -1.5924 x 10 -19 C, which is an excellent first measurement considering that the currently accepted measurement is -1.6022 x 10 -19 C.

Questions & Answers

Question: Why do we use oil and not water when determining the charge of an electron?

Answer: Millikan needed a liquid to produce droplets that would maintain their mass and spherical shape throughout the course of the experiment. To allow the droplets to be clearly observed, a light source was used. Water was not a suitable choice as water droplets would have begun evaporating under the heat of the light source. Indeed, Millikan chose to use a special type of oil that had a very low vapor pressure and would not evaporate.

Question: How was the value of 'n' calculated for the problem described in this article?

Answer: After performing the experiment, a histogram of electrical charges from the observed droplets is plotted. This histogram should roughly show a pattern of equally spaced clusters of data (demonstrating a quantized charge). Droplets within the lowest value cluster are assigned an 'n' value of one, droplets within the next lowest value cluster are assigned an 'n' value of two and so on.

Question: What is the acceleration of the droplet if the electric force is equal but opposite to that of gravity?

Answer: If the electrical force exactly balances the force of gravity the oil droplet's acceleration will be zero, causing it to float in mid-air. This is actually an alternative to the method of observing the droplet rise in an electric field. However, it is much more difficult to realize these conditions and observe a floating droplet, as it will still be undergoing random motion as a result of collisions with air molecules.

Question: How do the oil droplets acquire either the negative or the positive charge?

Answer: The electrical charge of the oil droplets is a convenient byproduct of how the oil is inserted into the cell. Oil is sprayed into the tube, during this spraying process some of the droplets will obtain a charge through friction with the nozzle (similar to the effect of rubbing a balloon on your head). Alternatively, the droplets could be given a charge by exposing the droplets to ionizing radiation.

© 2017 Sam Brind

Nwizzi chinwendu on January 29, 2020:

The best explanation

Wafula Eric on January 04, 2020:

Thanks for this well-detailed explanation. I really adored it

Ryan on October 21, 2019:

One of the best explanation to the topic.

Detailed and most importantly well structured and presented.

paul chukwualuka on September 25, 2019:

quite elaborate and detailed

samuel mutukiu on July 12, 2019:

its a wonderful explanation .The basis of Millikan's experiment is openly understood.

keith2019 on March 19, 2019:

It is a beautiful introduction about oil drop experiment. From background, theory to data analyses, it is quite clear.

Sam Brind (author) on March 08, 2019:

Like all other scientific experiments, the quantities involved are measured in SI units. For example: masses are measured in kilograms (kg), distances are measured in metres (m), forces are measured in Newtons (N) and electrical charges are measured in Coulombs (C).

ASE DAVID Alabokurogha on March 07, 2019:

good one but I still

need to know the basic units

professor kasirye on September 23, 2018:

this is really wonderful, I just liked it's simplicity

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Landmarks —Millikan Measures the Electron’s Charge

Landmarks articles feature important papers from the archives of the Physical Review journals.

Researchers now routinely isolate single electrons in quantum dots, but a century ago the state-of-the-art charge-trapping device was a droplet of clock oil. Robert Millikan’s oil drop experiment provided the first clear measurement of the fundamental electric charge and thus helped cement the notion that nature is “grainy” at the smallest level. The first results came out in 1910, but the seminal work was a 1913 paper in the Physical Review . Millikan reported a value for the fundamental electric charge that was within half a percent of today’s accepted value. The experiment helped earn Millikan a Nobel prize in 1923 but has been a source of some controversy over the years.

J. J. Thomson discovered the electron in 1897 when he measured the charge-to-mass ratio for electrons in a beam. But the value of the charge and whether it was fundamental remained open questions. Thomson and others tried to measure an irreducible electric charge by looking at clouds of water droplets. Using various techniques, they estimated the smallest charge that a droplet could hold, but the results were not entirely convincing because they relied on averages over many particles of various sizes. “The evidence for a unitary charge was at the time very ambiguous,” says science historian Gerald Holton of Harvard University.

At the University of Chicago in the 1900s, Millikan and his graduate students realized that ramping up the electric field would disperse a water cloud, so that only a few droplets remained. He decided to try isolating single droplets, but it soon became clear that single water droplets evaporated too quickly to make reliable measurements. One of his students, Harvey Fletcher, found that long-lasting droplets could be made with a light oil that was used for lubricating clocks.

The oil drop experiment that Millikan and Fletcher designed had two chambers. In the upper chamber, an atomizer (like that used in perfume bottles) dispersed a fine mist of micron-sized oil droplets. Individual droplets would fall through a pinhole into the lower chamber, which consisted of two horizontal plates, with one held 16 millimeters above the other. The air in this chamber was ionized with x rays , so that ions or free electrons could be captured on the falling droplets. A small window on the side allowed the scientists to observe the droplets through a telescope. The droplets fell slowly enough—due to atmospheric drag—that the researchers could measure their downward speed by eye, using horizontal lines in the telescope. From this speed, they could estimate the size and mass of each droplet.

They then applied a high voltage across the plates and measured the upward speed of the droplet, to determine the electric force and ultimately the charge. Multiple measurements on a single droplet could be performed by repeatedly turning the electric field on and off. The droplets had various amounts of charge on them (and they would often gain or lose charge during an observation), but the data showed that the charge was indeed quantized into integer multiples of a unit charge.

In 1910 Millikan published the first results of these experiments [1] (Fletcher was not included as an author, based on a deal the two struck [2] ). Millikan then made several improvements, including an empirical estimate of the drag forces. The culmination of this effort, reported in 1913, was a value of the fundamental charge with an error bar of just 0.2 percent. The precision acquired was so great that “other experiments did not improve on his result until a decade later,” Holton says.

But Felix Ehrenhaft of the University of Vienna repeatedly challenged Millikan’s results, based on his own measurements of “sub-electron” charges on small metal particles. The dispute lasted for many years—known as the “Battle over the Electron”—but eventually most physicists sided with Millikan.

In more recent years, historians who have examined Millikan’s lab notes have said that he discarded some of the measurements to boost the evidence of a fundamental charge. But David Goodstein of the California Institute of Technology in Pasadena believes these accusations of fraud are unwarranted. He has analyzed the notes and says that Millikan excluded droplets because their observations were incomplete, not because their implied charge didn’t match his expectations [3] . “Millikan’s oil drop experiment is a classic example of outstanding physics done by one of the giants of his era,” Goodstein says.

–Michael Schirber

Michael Schirber is a Corresponding Editor for Physics Magazine based in Lyon, France.

• R. A. Millikan, “The Isolation of an Ion, a Precision Measurement of its Charge, and the Correction of Stokes’s Law,” Science 32 , 436 (1910) ; first reported at the American Physical Society meeting, 23 April 1910, Phys. Rev. (Series I) 30 , 656 (1910)
• H. Fletcher, “My work with Millikan on the oil‐drop experiment,” Phys. Today 35 , 43 (1982)
• D. Goodstein, “In Defense of Robert Andrews Millikan,” Am. Sci. 89 , 54 (2001)

More Information

Focus story on Millikan’s measurement of Planck’s constant

article by Gerald Holton on the Millikan-Ehrenhaft Dispute

article about the ethics of Millikan’s handling of data

Millikan Nobel Prize: Nobel lecture, biography, and other information

On the Elementary Electrical Charge and the Avogadro Constant

R. A. Millikan.

Phys. Rev. 2 , 109 (1913)

Published August 1, 1913

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• Millikan's Oil Drop Experiment

Introduction

The oil drop experiment was performed in 1909 by Robert A. Millikan and Harvey Fletcher to measure the elementary electric charge (it means the electron's charge). This experiment took place in the Ryerson Physical Laboratory, which is present at the University of Chicago. Also, this experiment has proved to be very crucial in physics.

Before this experiment, the existence of subatomic particles was not accepted universally. Millikan's apparatus has an electric field created between a parallel pair of metal plates held apart by an insulating material. The oil droplets, which are electrically charged, enter the electrical field and are balanced between two plates by altering the field. When the charged drops fell at a constant rate, the gravitational forces and electric forces on it were equal.

Principles of Millikan's Experiment

The Millikan experiment is complicated and fiddly while performing in school. It is more likely that we will use a simulation or a film clip of the experiment to show its principles to the students. Few of such principles are,

An oil drop can fall under its own weight. If a charge is given to the drop, it can be suspended by using an electric field. At this point, the electrostatic force balances the weight of every drop. Then the size of the electrostatic force depends entirely on the drop. So Millikan should have figured out the charge as soon as he knew the weight.

Millikan allowed the drop to fall through the air to find the weight of the drop. It reaches its terminal velocity quickly. At this point, the weight is balanced by the viscous drag of the air. Drag can be calculated from the Stokes' Law, which allowed Millikan to determine the weight.

Millikan repeated the same experiment thoroughly for over 150 oil drops and selected 58 of Millikan oil drop experiment results and got to find the highest common factor. It means the single unit of charge that could be multiplied up to give the charge he measured on all of his oil drops.

Oil Drop Experiment

Millikan allowed charged small oil droplets to travel through a hole into an electric field in the experiment. With the electric field's varying strength, the charge over an oil droplet is calculated, and it always comes as a fundamental value of 'e.'

(Image will be uploaded soon)

Millikan and Fletcher designed the experiment apparatus. It included two metal plates held at a distance by an insulated rod. There were four holes in the plate, three of which were there to allow light to pass through, and one was there to allow viewing through the microscope.

They did not use ordinary oil for this experiment, as it would evaporate by the heat of the light, and could cause an error in the Millikan Oil Drop Experiment. The oil, which is usually used in a vacuum apparatus with low vapour pressure, was also used.

Oil passes through the atomizer, from where it came in tiny droplets form. The same droplets pass through the holes in the upper plate of the apparatus.

The droplet's downward movements are observed through the microscope and the mass of the oil droplets, and then their terminal velocity is measured.

The air present inside the chamber is ionised by passing through the X-ray beam. Collisions obtain the electrical charge on these oil droplets with gaseous ions produced by the ionisation of air.

Then, the electric field is set up between the two plates so that the motion of the charged oil droplets can be affected by the same electric field.

Now, gravity attracts the oil in a downward direction, and the electric field pushes the charge upwards. Also, the electric field strength is regulated so that all the oil droplets reach an equilibrium position with gravity.

The charge on the droplet is calculated at equilibrium, which depends on the mass of the droplet and strength of the electric field.

Millikan Oil Drop Experiment Calculations

The experiment initially allows the oil drops to fall between the plates in the absence of the electric field. They accelerate first due to gravity, but gradually the oil droplets slow down because of air resistance.

The Millikan oil drop experiment formula can be given as below.

F up = Q ⋅ E   F down = m

Where Q is an electron’s charge, m is the droplet’s mass, E is the electric field, and g is gravity.

Q ⋅ E = m ⋅ g

By this, one can identify how an electron charge is measured by Millikan. Millikan also found that all the drops had charges, which were 1.6x 10 -19 C multiples.

Importance of Millikan's Oil Drop Experiment

Millikan's experiment is quite essential because it establishes the charge on an electron.

Millikan used a simple apparatus in which he balanced the actions of electric, gravitational, and air drag forces.

Using the apparatus, he was able to calculate the charge on an electron as 1.60 × 10 -19 C.

The charge for any oil droplet is always an integral value of e (1.6 x 10 -19 ). Thus, Millikan's Oil Drop Experiment concludes that the charge is said to be quantized, which means that the charge on any particle will be an integral multiple of e always.

Millikan discovered the charge on a single electron using a uniform electric field between the oil drops and two parallel charged plates.

FAQs on Millikan's Oil Drop Experiment

1. What is Millikan’s Oil Drop experiment?

In 1909, Robert Millikan and Harvey Fletcher conducted the canvas drop trial to determine the charge of an electron. They suspended bitsy charged driblets of canvas between two essence electrodes by balancing downcast gravitational force with upward drag and electric forces. The viscosity of the canvas was known, so Millikan and Fletcher could determine the driblets’ millions from their observed diameters (since from the diameters they could calculate the volume and therefore, the mass). Using the known field and therefore the values of graveness and mass, Millikan and Fletcher determined the charge on canvas driblets in mechanical equilibrium. By repeating the trial, they verified that the charges were all multiples of some abecedarian value. They calculated this value to be1.5924 × 10 −19 Coulombs (C), which is within 1 of the presently accepted value of1.602176487 × 10 −19 C. They proposed that this was the charge of one electron.

2. How did the process work?

The outfit incorporated a brace of essence plates and a specific type of canvas. Millikan and Fletcher discovered it had been stylish to use a canvas with a particularly low vapor pressure, similar together designed to be used during a vacuum outfit. Ordinary canvas would dematerialize under the heat of the light source, causing the mass of the canvas to drop to change over the course of the trial.

By applying an implicit difference across a resemblant brace of vertical essence plates, an invariant electric field was created in the space between them. A ring of separating material was used to hold the plates piecemeal. Four holes were dug into the ring — three for illumination by a bright light and another to permit viewing through a microscope. A fine mist of canvas driblets was scattered into a chamber above the plates. The canvas drops came electrically charged through disunion with the snoot as they were scattered. Alternatively, the charge could be convinced by including an ionizing radiation source ( similar to an X-ray tube).

3. Describe the Millikan’s Oil Drop experiment procedure?

Canvas is passed through the atomizer from where it came in the form of bitsy driblets. They pass the driblets through the holes present in the upper plate of the outfit.

The downcast movements of driblets are observed through a microscope and the mass of canvas driblets also measure their terminal haste.

The air inside the chamber is ionised by passing a ray of X-rays through it. The electrical charge on these canvas driblets is acquired by collisions with gassy ions produced by the ionisation of air.

The electric field is set up between the two plates and so the stir of charged canvas driblets can be affected by the electric field.

Graveness attracts the canvas in a downcast direction and the electric field pushes the charge overhead. The strength of the electric field is regulated so that the canvas drop reaches an equilibrium position with graveness.

The charge over the drop is calculated at equilibrium, which depends on the strength of the electrical field and the mass of the drop.

4. Explain Millikan’s Oil Drop experiment in detail?

Millikan’s original trial or any modified interpretation, similar to the following, is called the canvas-drop trial. An unrestricted chamber with transparent sides is fitted with two resemblant essence plates, which acquire a positive or negative charge when an electric current is applied. At the launch of the trial, an atomizer sprays a fine mist of canvas driblets into the upper portion of the chamber. Under the influence of gravity and air resistance, some of the canvas driblets fall through a small hole cut in the top essence plate. When the space between the essence plates is ionized by radiation (e.g., X-rays), electrons from the air attach themselves to the falling canvas driblets, causing them to acquire a negative charge. 

A light source, set at right angles to a viewing microscope, illuminates the canvas driblets and makes them appear as bright stars while they fall. The mass of a single charged drop can be calculated by observing how presto it falls. By confirming the implicit difference, or voltage, between the essence plates, the speed of the drop’s stir can be increased or dropped; when the quantum of upward electric force equals the given downcast gravitational force, the charged drop remains stationary. The quantum of voltage demanded to suspend a drop is used along with its mass to determine the overall electric charge on the drop.

Through the repeated operation of this system, the values of the electric charge on individual canvas drops are always whole- number multiples of the smallest value — that value being the abecedarian electric charge itself (about1.602 × 10 −19 coulomb). From the time of Millikan’s original trial, this system offered satisfying evidence that electric charge exists in introductory natural units. All posterior distinct styles of measuring the introductory unit of electric charge point to its having the same abecedarian value. 

5. How does Millikan’s Oil Drop experiment work?

Simplified scheme of Millikan’s canvas-drop trial This outfit has a resemblant brace of vertical essence plates. An invariant electric field is created between them. The ring has three holes for illumination and one for viewing through a microscope. A specific type of canvas is scattered into the chamber, where drops come electrically charged. The driblets enter the space between the plates and can be controlled by changing the voltage across the plates. 

The driblets entered the space between the plates and, because they were charged, they could be controlled by changing the voltage across the plates. Originally, the canvas drops were allowed to fall between the plates with the electric field turned off. The snappily reached terminal haste due to disunion with the air in the chamber. The field was turned on and, if it was large enough, some of the drops (the charged bones) would start to rise. This is because the overhead electric force, FE, is lesser for them than the down gravitational force,g. (A charged rubber rod can pick up bits of paper in the same way.) A likely-looking drop was named and kept in the middle of the field of view by alternatively switching off the voltage until all the other drops fell. The trial was continued with this single drop. Millikan’s canvas drop trial measured the charge of an electron. Before this trial, the actuality of subatomic patches wasn't widely accepted. 

Millikan’s outfit contained an electric field created between a resemblant brace of essence plates, which were held piecemeal by separating material. Electrically charged canvas driblets entered the electric field and were balanced between two plates by altering the field. 

6. Why was the Negative Plate Earthed in Millikan's Oil Drop Experiment?

There are three possible reasonable ways to clear it.

The first reason is safety. Grounding ("earthing," in this context), the equipment is so important, particularly the time when you are working with high voltages. The same would be applied to protecting the equipment and for personal safety as well.

The second reason would be to establish a good stable reference point for the voltage measurement. A massive and solidly connected grounding cable would perform that job in a better way.

Finally, from an electrical standpoint, the two plates used in Millikan's experiment form a capacitor. On the other side, this capacitor is being charged to a very high voltage. In such cases, it is suggested to have a discharge path on one of the terminals or plates in order to avoid damage to either humans or equipment as well. Therefore, the negative plate is earthed.

7. Why do we Use Oil Instead of Other Liquids in the Millikan Oil-drop Experiment?

Oil is one of the best liquids for Millikan's oil drop experiment. It retains its mass over a while and exposes to higher temperatures. Also, we employ an atomizer for ultra-fine droplets. So less dense liquids like water and oils are preferred over water because water cannot survive at such higher temperatures.

The atomizer employment is also an important reason behind using oil for this experiment. Moreover, it should be noted that oil would retain the exact volume/mass/weight. This would enable an exact measurement of the charge. Other liquids would separate or dissipate or even evaporate.

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Chapter 2 Electric Charge and Electric Field

2.2 Discovery of the Parts of the Atom: Electrons and Nuclei – Millikan Oil Drop Experiment and Rutherford Scattering

• Describe how electrons were discovered.
• Explain the Millikan oil drop experiment.
• Describe Rutherford’s gold foil experiment.
• Describe Rutherford’s planetary model of the atom.

Just as atoms are a substructure of matter, electrons and nuclei are substructures of the atom. The experiments that were used to discover electrons and nuclei reveal some of the basic properties of atoms and can be readily understood using ideas such as electrostatic and magnetic force, already covered in previous chapters.

Charges and Electromagnetic Forces

In previous discussions, we have noted that positive charge is associated with nuclei and negative charge with electrons. We have also covered many aspects of the electric and magnetic forces that affect charges. We will now explore the discovery of the electron and nucleus as substructures of the atom and examine their contributions to the properties of atoms.

The Electron

Gas discharge tubes, such as that shown in Figure 1 , consist of an evacuated glass tube containing two metal electrodes and a rarefied gas. When a high voltage is applied to the electrodes, the gas glows. These tubes were the precursors to today’s neon lights. They were first studied seriously by Heinrich Geissler, a German inventor and glassblower, starting in the 1860s. The English scientist William Crookes, among others, continued to study what for some time were called Crookes tubes, wherein electrons are freed from atoms and molecules in the rarefied gas inside the tube and are accelerated from the cathode (negative) to the anode (positive) by the high potential. These “ cathode rays ” collide with the gas atoms and molecules and excite them, resulting in the emission of electromagnetic (EM) radiation that makes the electrons’ path visible as a ray that spreads and fades as it moves away from the cathode.

Gas discharge tubes today are most commonly called cathode-ray tubes , because the rays originate at the cathode. Crookes showed that the electrons carry momentum (they can make a small paddle wheel rotate). He also found that their normally straight path is bent by a magnet in the direction expected for a negative charge moving away from the cathode. These were the first direct indications of electrons and their charge.

But the vertical deflection is also related to the electron’s mass, since the electron’s acceleration is

The value of  the force F   is not known, since q e   was not yet known. Substituting the expression for electric force into the expression for acceleration yields

Gathering terms, we have

This is a huge number, as Thomson realized, and it implies that the electron has a very small mass. It was known from electroplating that about 10 8 C/kg  is needed to plate a material, a factor of about 1000 less than the charge per kilogram of electrons. Thomson went on to do the same experiment for positively charged hydrogen ions (now known to be bare protons) and found a charge per kilogram about 1000 times smaller than that for the electron, implying that the proton is about 1000 times more massive than the electron. Today, we know more precisely that

Thomson performed a variety of experiments using differing gases in discharge tubes and employing other methods, such as the photoelectric effect, for freeing electrons from atoms. He always found the same properties for the electron, proving it to be an independent particle. For his work, the important pieces of which he began to publish in 1897, Thomson was awarded the 1906 Nobel Prize in Physics. In retrospect, it is difficult to appreciate how astonishing it was to find that the atom has a substructure. Thomson himself said, “It was only when I was convinced that the experiment left no escape from it that I published my belief in the existence of bodies smaller than atoms.”

Thomson attempted to measure the charge of individual electrons, but his method could determine its charge only to the order of magnitude expected.

In the Millikan oil drop experiment, fine drops of oil are sprayed from an atomizer. Some of these are charged by the process and can then be suspended between metal plates by a voltage between the plates. In this situation, the weight of the drop is balanced by the electric force:

The electric field is produced by the applied voltage, hence,  E =V/d , and  V is adjusted to just balance the drop’s weight. The drops can be seen as points of reflected light using a microscope, but they are too small to directly measure their size and mass. The mass of the drop is determined by observing how fast it falls when the voltage is turned off. Since air resistance is very significant for these submicroscopic drops, the more massive drops fall faster than the less massive, and sophisticated sedimentation calculations can reveal their mass. Oil is used rather than water, because it does not readily evaporate, and so mass is nearly constant. Once the mass of the drop is known, the charge of the electron is given by rearranging the previous equation:

where d is the separation of the plates and V  is the voltage that holds the drop motionless. (The same drop can be observed for several hours to see that it really is motionless.) By 1913 Millikan had measured the charge of the electron q e  to an accuracy of 1%, and he improved this by a factor of 10 within a few years to a value of  -1.60 x  10 -19 C . He also observed that all charges were multiples of the basic electron charge and that sudden changes could occur in which electrons were added or removed from the drops. For this very fundamental direct measurement of q e   and for his studies of the photoelectric effect, Millikan was awarded the 1923 Nobel Prize in Physics.

https://www.nobelprize.org/prizes/physics/1923/summary/

With the charge of the electron known and the charge-to-mass ratio known, the electron’s mass can be calculated. It is

Substituting known values yields

or                                                               m e = 9.11 x 10 – 31   kg

where the round-off errors have been corrected. The mass of the electron has been verified in many subsequent experiments and is now known to an accuracy of better than one part in one million. It is an incredibly small mass and remains the smallest known mass of any particle that has mass. (Some particles, such as photons, are massless and cannot be brought to rest, but travel at the speed of light.) A similar calculation gives the masses of other particles, including the proton. To three digits, the mass of the proton is now known to be

Another important characteristic of quantum mechanics was also beginning to emerge. All electrons are identical to one another. The charge and mass of electrons are not average values; rather, they are unique values that all electrons have. This is true of other fundamental entities at the submicroscopic level. All protons are identical to one another, and so on.

The Nucleus

Here, we examine the first direct evidence of the size and mass of the nucleus. In later chapters, we will examine many other aspects of nuclear physics, but the basic information on nuclear size and mass is so important to understanding the atom that we consider it here.

Nuclear radioactivity was discovered in 1896, and it was soon the subject of intense study by a number of the best scientists in the world. Among them was New Zealander Lord Ernest Rutherford, who made numerous fundamental discoveries and earned the title of “father of nuclear physics.” Born in Nelson, Rutherford did his postgraduate studies at the Cavendish Laboratories in England before taking up a position at McGill University in Canada where he did the work that earned him a Nobel Prize in Chemistry in 1908. In the area of atomic and nuclear physics, there is much overlap between chemistry and physics, with physics providing the fundamental enabling theories. He returned to England in later years and had six future Nobel Prize winners as students. Rutherford used nuclear radiation to directly examine the size and mass of the atomic nucleus. The experiment he devised is shown in Figure 7 . A radioactive source that emits alpha radiation was placed in a lead container with a hole in one side to produce a beam of alpha particles, which are a type of ionizing radiation ejected by the nuclei of a radioactive source. A thin gold foil was placed in the beam, and the scattering of the alpha particles was observed by the glow they caused when they struck a phosphor screen.

PhET simulation.  Direct link:   https://phet.colorado.edu/sims/html/rutherford-scattering/latest/rutherford-scattering_en.html 

Alpha particles were known to be the doubly charged positive nuclei of helium atoms that had kinetic energies on the order of  5 MeV   when emitted in nuclear decay, which is the disintegration of the nucleus of an unstable nuclide by the spontaneous emission of charged particles. These particles interact with matter mostly via the Coulomb force, and the manner in which they scatter from nuclei can reveal nuclear size and mass. This is analogous to observing how a bowling ball is scattered by an object you cannot see directly. Because the alpha particle’s energy is so large compared with the typical energies associated with atoms  MeV  versus eV (in other words 1 million times greater) , you would expect the alpha particles to simply crash through a thin foil much like a supersonic bowling ball would crash through a few dozen rows of bowling pins. Thomson had envisioned the atom to be a small sphere in which equal amounts of positive and negative charge were distributed evenly. The incident massive alpha particles would suffer only small deflections in such a model. Instead, Rutherford and his collaborators found that alpha particles occasionally were scattered to large angles, some even back in the direction from which they came! Detailed analysis using conservation of momentum and energy—particularly of the small number that came straight back—implied that gold nuclei are very small compared with the size of a gold atom, contain almost all of the atom’s mass, and are tightly bound. Since the gold nucleus is several times more massive than the alpha particle, a head-on collision would scatter the alpha particle straight back toward the source. In addition, the smaller the nucleus, the fewer alpha particles that would hit one head on.

Although the results of the experiment were published by his colleagues in 1909, it took Rutherford two years to convince himself of their meaning. Like Thomson before him, Rutherford was reluctant to accept such radical results. Nature on a small scale is so unlike our classical world that even those at the forefront of discovery are sometimes surprised. Rutherford later wrote: “It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you. On consideration, I realized that this scattering backwards … [meant] … the greatest part of the mass of the atom was concentrated in a tiny nucleus.” In 1911, Rutherford published his analysis together with a proposed model of the atom. The size of the nucleus was determined to be about  10 -15 m , or 100,000 times smaller than the atom. This implies a huge density, on the order of  10 -15   g / cm 3    , vastly unlike any macroscopic matter. Also implied is the existence of previously unknown nuclear forces to counteract the huge repulsive Coulomb forces among the positive charges in the nucleus. Huge forces would also be consistent with the large energies emitted in nuclear radiation.

The small size of the nucleus also implies that the atom is mostly empty inside. In fact, in Rutherford’s experiment, most alphas went straight through the gold foil with very little scattering, since electrons have such small masses and since the atom was mostly empty with nothing for the alpha to hit. There were already hints of this at the time Rutherford performed his experiments, since energetic electrons had been observed to penetrate thin foils more easily than expected. Figure 8 shows a schematic of the atoms in a thin foil with circles representing the size of the atoms (about  10 -10 m  and dots representing the nuclei. (The dots are not to scale—if they were, you would need a microscope to see them.) Most alpha particles miss the small nuclei and are only slightly scattered by electrons. Occasionally, (about once in 8000 times in Rutherford’s experiment), an alpha hits a nucleus head-on and is scattered straight backward.

Based on the size and mass of the nucleus revealed by his experiment, as well as the mass of electrons, Rutherford proposed the planetary model of the atom . The planetary model of the atom pictures low-mass electrons orbiting a large-mass nucleus. The sizes of the electron orbits are large compared with the size of the nucleus, with mostly vacuum inside the atom. This picture is analogous to how low-mass planets in our solar system orbit the large-mass Sun at distances large compared with the size of the sun. In the atom, the attractive Coulomb force is analogous to gravitation in the planetary system. (See Figure 9 .) Note that a model or mental picture is needed to explain experimental results, since the atom is too small to be directly observed with visible light.

Rutherford’s planetary model of the atom was crucial to understanding the characteristics of atoms, and their interactions and energies, as we shall see in the next few sections. Also, it was an indication of how different nature is from the familiar classical world on the small, quantum mechanical scale. The discovery of a substructure to all matter in the form of atoms and molecules was now being taken a step further to reveal a substructure of atoms that was simpler than the 92 elements then known. We have continued to search for deeper substructures, such as those inside the nucleus, with some success. In later chapters, we will follow this quest in the discussion of quarks and other elementary particles, and we will look at the direction the search seems now to be heading.

PhET Explorations: Rutherford Scattering

How did Rutherford figure out the structure of the atom without being able to see it? Simulate the famous experiment in which he disproved the Plum Pudding model of the atom by observing alpha particles bouncing off atoms and determining that they must have a small core.

Section Summary

• Atoms are composed of negatively charged electrons, first proved to exist in cathode-ray-tube experiments, and a positively charged nucleus.
• All electrons are identical and have a charge-to-mass ratio of q e  / m e   = 1.76 x 10 11    C/kg
• The positive charge in the nuclei is carried by particles called protons, which have a charge-to-mass ratio of                            q p  / m p   = 9.57 x 10 7    C/kg
• Mass of electron, m e = 9.11  x 10 -31 kg
• Mass of proton, m p  = 1.67  x 10 -27 kg
• The planetary model of the atom pictures electrons orbiting the nucleus in the same way that planets orbit the sun.

Conceptual Questions

1: What two pieces of evidence allowed the first calculation of m e , the mass of the electron?

(a) The ratios q e / m e and q p /m p

(b) The values  q e   and  E/B

(c) The ratio  q e / m e and  q e  

Justify your response.

2: How do the allowed orbits for electrons in atoms differ from the allowed orbits for planets around the sun? Explain how the correspondence principle applies here.

Problem Exercises

1: Rutherford found the size of the gold nucleus to be about  10 -15 m.  This implied a huge density. What would this density be for gold?

2:  In Millikan’s oil-drop experiment, one looks at a small oil drop held motionless between two plates. Take the voltage between the plates to be 2033 V, and the plate separation to be 2.00 cm. The oil drop of density 810 kg / m 3   has a diameter 4.0  x 10 -6 m . Find the charge on the drop, a) in coulombs and then b) in terms of electron units.

3: (a) An aspiring physicist wants to build a scale model of a hydrogen atom for her science fair project. If the atom is 1.00 m in diameter, how big should she try to make the nucleus?   Assume the diameter of the hydrogen nucleus is 1 x 10 -15 m while that of the atom is 1 angstrom or 1 x 10 -10 m.

(b) How easy will this be to do?

1:   6  x  10 20 {kg/m}^3

2: In Millikan’s oil-drop experiment, one looks at a small oil drop held motionless between two plates. Take the voltage between the plates to be 2033 V, and the plate separation to be 2.00 cm. The oil drop of density 810 kg / m 3   has a diameter 4.0 x 10 -6 m . Find the charge on the drop, in terms of electron units.

2:  Worked out answer:   density = mass / volume so  mass = (density) ( volume ) = (density) ( 4 / 3  π  r 3 )

mass =  2.17 x 10 -14  kg

net force = 0 N as it is suspended   gravity force = electric force     m g = q E  = q (Voltage/gap width)

q = m g d / Voltage  = 2.09 x 10 – 17 C

a) 2.09 x 10 -18 C  b) 13 electrons

3: (a) 1 x 10 -5 m = 10 x 10 -6 m = 10 microns = 10 μm

(b) It isn’t hard to make one of approximately this size. It would be harder to make it exactly 10 μm.

Douglas College Physics 1207 Copyright © August 22, 2016 by OpenStax is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.