Download The Historical and Conceptual Development of

“The Historical and Conceptual Development of the Electron”
And
“Measuring the Fundamental Electric Charge”
Development of Ideas in Physical Science
Fall 2005
Professor Etkina
Joseph Santonacita
Jeffrey Goett
The Historical and Conceptual Development of the Electron
A firm construct of the atomic theory had been developed via chemical evidence and the kinetic
theory of matter. The electrical nature of matter was also firmly developed. However the link
between electrical and atomic nature of the atom was not clearly recognized or understood. A
number of people, JW Hittorf, Sir Williams Crookes, Eugene Goldstein, and Jean Baptiste Perrin
attempted to link the path between electrical and atomic nature of discharged gas.
For each case the method and results were generally similar. A glass tube with platinum
electrode was partially evacuated while a large potential difference was applied between the
electrodes.
Fig A. Cathode ray apparatus, using Geissler tube. The tube contained small traces of gas that
would be ionized.
The visible gas discharge was then studied as a function of pressure, electric field and the nature
of gas. At the time, it was known that these discharges from the cathode exhibited interesting
properties. The most significant was green florescence produced in the glass walls when
radiation fell upon them. These experiments all yielded similar results: qualitative observations
of the gas discharge phenomena.
There was much discussion and interest into what cause this phosphorescent discharge. Initially
people thought cathode rays were some form of electromagnetic waves or ether disturbance.
Below outlines some of the major conceptual developments via observational experiments to
identify the properties of cathode rays.
Notable Developments:
0. Faraday via research in electrochemical decomposition Faraday established all the
modern terminology: electrode, cathode, anode, ion, anion, cation, and electrolyte utilized
in a Geissler/Crookes tube. Faraday first established that a current with an electrical
charge could be deflected by a magnetic field and vise versa. He established the idea a
definite charge quantity of electricity is associated with each atom of matter in his law of
electrochemistry decomposition. In 1838 he when a good enough vacuum was available
investigated the cathode rays in a vacuum, which was the primary way cathode rays were
to be investigated.
1. Maxwell via Faraday’s law of electrolysis correctly identified that one could calculate the
electrical charge of an elementary “atom” but found the feat to be a difficult task and did
not attempt it. He stated each ion is charge with certain electrical charge of a “molecular
charge” which would be “the most natural unit of electricity”
1a. Johnstone Stoney: 1874 use the value of Avogadro’s number which he himself had
estimated to calculate the charge of this particle to be 10-20 Coulomb (1/16th of the modern
value) In an article published in 1894 Stoney coined the phrase electron.
2. Technological Advances: the Vacuum Pump: Johann Heinrich Wilhelm Geissler who
created a new vacuum pump and Hermann Sprengel who improved upon it. This yielded
better vacuums, which were utilized the study of cathode rays.
3. Geissler, a glassmaker and mechanical technician provide instruments for mathematician
–physicist Julius Plucker at the University of Bonn. Geissler became interested in
studying vapors at low pressures after he constructed the vaporimeter, an instrument to
measure the alcoholic strength of wine by determining the vapor pressures of alcohol and
air. This was done to test the alcoholic strength of wine. Geissler created mercury vapor
pump in 1855 which enabled him to create small glass tubes with electrodes melted into
the ends fill with gasses at very low pressures, which became known as Geissler tubes.
(see Fig A).
4. Julius Plucker (1858): Plucker utilized the tubes to pursue Faraday’s study and found at
the lower pressures the inside of the tube became darker and darker and there was an
extended glow on the glass walls around the cathode. He also found the cathode rays
were influenced by a magnetic presence.
5. JW. Hittorf (1869): Found that the most intense glow occurred in an L shaped tube
occurred directly across from the cathode which suggested that the glow was not attracted
to the anode. By creating a L-shaped tube Hittorf established that these invisible rays
seemed to travel in straight line from the cathode to the glass wall. When it hit the glass
wall the collision produced a phosphorescence glow. Hittorf found that any solid body
placed in front of the cathode cut off the glow on the surrounding walls. The glow
propagated in a straight line. Hittrof also noted that the glow was influenced by a
magnetic field.
 Green phosphorescence glow
Fig 2. A bent Geissler tube with green phosphorescence glow hitting the glass.
6. Goldstein (1870s): coined the word “cathode rays”, and held the belief that the radiation
produced was a wave phenomena similar to light. Eugene Goldstein established the
cathode rays are emitted perpendicular to the surface of a cathode, can cast sharp
shadows, produce chemical reactions and are independent of the nature of the cathode.
7. Cromwell Fleetwood Varley (1871): first to come to the conclusion that particles were
negatively charged by observing that negatively charged particles would be deflected the
same way in the magnetic field.
8. Crookes: demonstrated rectilinear propagation of the radiation by placing obstacles
between the cathode and the glass wall showing by “showing” optical properties.
Crookes utilized a bent Geisseler tube (Fig 2) and found the most intense green glow
appeared on the part of the tube directly opposite the cathode, as if the rays were being
repelled away from the anode. He explained this by stating the particles of the gas in the
tube collided with the cathode and became negatively charged. Since the cathode and the
particles were negatively charged they were then repulsed perpendicular to the cathode.
This explained most of the rays behavior in the tube. The rays did not seem to be affected
by an electric field however they were affected by a magnetic field. Crookes found that
any solid body placed in front of the cathode cut off the glow on the surrounding glass
walls, as if it were blocking some kid of rays propagating from the cathode. This was
demonstrated in his now infamous Maltese Cross Crooke’s tube with the cross acting as
the anode (Fig 3 -5). Crookes purposed in 1879 that the ray’s molecules that have
attained a negative electric charge and are repelled away from the field.
Fig. 3
Fig. 4
Fig 5
Fig 3 -5: Figures 3 and 4 are modern Crooke’s tubes with Maltese Crosses lit up with
cathode rays. Figure 5 is a drawing of Crooke’s observations.
9. Peter Gutheir Tait (1880): Noticed that the illumination of the walls and the light emitted
by them should display the Doppler effect. It did not.
10. Arthur Schuster (1884): Suggested that the light might be produced by the interaction
with the gas that is struck by the cathode rays. That is why he stated the Doppler affect
does not occur. Calculated the limits for maximum and minimum values of q/m.
Theorized his own schematic for the propagation of cathode rays, stating it was a
function of the gas disassociating with the positive parts being attracted to the cathode
and the negative parts to the anode.
11. In a damning observation by a prominent figure Hertz did not observe the bending of the
stream of particles in an electric field. Hertz’s understudy was Lenard who also took up
the Giessler tube and began examining this discharge and discovered that if the end of the
tube was covered in Aluminum, instead of glass the discharge passed through the
aluminum into the air for a few centimeters then dissipated. Hertz held tightly, along
with the rest of Germany to the belief the cathode rays were electromagnetic waves in
ether. His influence and belief in the cathode rays wave nature persisted until Thomson
corrected his error which was that Hertz needed a mostly evacuated tube.
12. Jean Perrin found that a neutral object assumed a negative charge when cathode rays fell
upon it, believing the radiation is corpuscular. (see Thompson’s Experiment for detailed
explanation)
What were different explanations of what cathode rays were?
So what were these cathode rays comprised of? One might suppose the Plucker and Hittorf
considered the possibility that they are some kind of atomic particles. The first published
suggestion along these lines is attributed to Cromwell Fleetwood Varley, who said they are
composed of “attenuated particles of matter projected from the negative pole by electricity in
all directions” The German led by Hertz held tightly to the belief that cathode rays were
some sort of electromagnetic wave. While the English believed the cathode rays were some
type of ion. As more discoveries the process evolved along with the ideas, Thomson, found
the conceptual flaws in previous experiments and with indirect help from Roentgen put the
pieces together in one coherent whole.
13. Roentgen : demonstrated that when x-rays pass through the air, the air itself becomes
electrically charged. Roentgen discovered the X-Ray originate from the tube. He was
attempting to reexamine the work of Hertz’s understudy Lenard in placing aluminum into
the into the Crookes tube. In attempting to isolate the tube so he could study the
discharge of electrified bodies. As a great potential difference was created in a dark room
he noticed as he was walking back that a barium platinocyanide screen lying about a
meter away became mysteriously fluorescent. The screen was originally used to detect
ultraviolet light. However since the box is covered in cardboard, no ultraviolet light
would pass through the cardboard. While Roentgen was excited but did not know
anything about this mysterious color or precisely what was causing it. Roentgen felt the
emission was radiation and not a cathode ray. So like any good scientists he began to
experiment for seven weeks he locked himself away investigating the properties of the
mysterious x-rays.
Figure 6.
Physical Institute laboratory room in which
Roentgen first noted and investigated X-rays.
After experimenting Roentgen discovered X-rays were created where the cathode rays interacted
with the glass. After his initial investigation, Roentgen demonstrated that the x-rays possessed
many properties of electromagnetic waves, but he could not get them to diffract. After this time,
Roentgen also produced an X-ray photograph of his wife’s hand. In the process he
revolutionized modern medicine and injected a flurry of interest in scientific exploration. He had
captured the world’s attention with his X-rays.
Figures 7-9
(7)
(8)
(9)
Fig 7: One of a series of experimental radiographs made by Roentgen to determine the ability of
the rays to penetrate various solids.
Fig 8: The famous radiograph made by Roentgen on Dec. 22, 1895, and sent to physicist Franz
Exner in Vienna. This is traditionally known as "the first X-ray picture" and "the radiograph of
Mrs. Roentgen's hand.
Fig 9: Radiograph of the hand of Albert von Kolliker, made at the conclusion of Roentgen's
lecture and demonstration at the Wurzburg Physical-Medical Society on Jan. 23, 1896.
In Roentgen’s second communication on the investigation of X-rays examine the air or
any other gas which has been exposed to X-rays could conduct electricity and would
discharge an electrically charged body. It was this paper and Roentgen’s observations were
significant in the process of the discovery of the electron. Roentgen observed that the air
ionized as x-rays passed through them. A charged electroscope attracted to the x-rays lost its
charge, as the newly created ions in the air were attracted to the charged leaves.
All these observations and debates about the nature of the radiation continued until Thomson
proved the particles originated by the cathode. How did he do this? Roentgen’s discovery was
indirectly significant because Thompson was able to utilize Roentgen’s work as a means of
investigating the conduction of gas. Thompson was able to extract that current was carried by
positive and negative ions, such as would be expected if the x-rays disrupted the molecule of gas.
These observation led Thomson to devise telling experiments on electrical discharges in rarified
gases, and from these identify the electron as the unit of electrical charge.
Thomson’s Experiment
After a careful reexamination and line of reason of his peers, in particular that of Perrin and of
Hertz Thomson drew a number of conclusions, some of which were readily apparent to others in
the field.
In examining Perrin experiment of shooting cathode rays at an electroscope Thomson concluded
that the rays which are emitted perpendicular from the cathode are charged with negative
electricity. However, it does not prove this experiment electrification has anything to do with the
cathode. Thomson tweaks Perrin’s experiment and aims the cathode rays away from the
electroscope then utilizes a magnet to bend the rays towards the electroscope. Here the
electroscope becomes charged.
Here Thomson goes into detail about the gas becoming a conductor (from the observations of
Roentgen) when the cathode ray passes through it. The electrometer does not continually
increase its charge as the rays keep passing through it. As the rays pass through the bulb the gas
inside becomes a conductor. As they travel down to the electrometer (electroscope), in inner
cylinder, there is a connected passage way to the earth, the outer cylinder. As the cathode rays
pass though the two cylinders, the air between them becomes conductive and electricity escapes
from the inner cylinder to the earth. Here Thomson meticulously reassures his reasoning by
repeating Perrin’s experiment with a little twist proving the cathode rays are negatively charged.
Figure 11: Perrin’s Crooke’s Tube with Electroscope
The inner tube is connected to the electrometer in the figure above and the outer tube, earth.
Later on in Thomson paper he explains the creation of the cathode rays which will be examined
now. In the extreme intensity of the electric field surround the immediate area of the cathode has
a profound effect on the gas molecules surrounding it. The molecules of gas are disassociated
and split up, breaking down into “primordial parts” (subatomic particles), with the focus on
corpuscles (electrons). The corpuscles are charged with electricity and projected away from the
cathode (presumably of the same charge) and act as cathode rays. Thomson then goes on to
explain the rate at which travel through the tube is proportional to the number of gas molecules
and interactions to other corpuscles it has on the way.
Next Thomson reexamined the experiments of Hertz. Thomson passed the cathode rays through
an electric field and the results were the same as Hertz, no deflection. But following experiments
showed that the deflection was passed upon the conductivity properties of the rarefied gas. The
vacuum is well established in the tube, Thomson observed the deflection of the rays. However
over time this deflection broke down. Thomson explain this through an analogy, if the two
plates attracted oppositely charged ions, it would slowly break down the electric field between
the plates and the electrical intensity between the plates would vanish. Other observations
include when the ray jumped back to the initial position and a bright discharge passes through
the plates when the residual air breaks down between the plates.
Thompson reasons: as the cathode rays carry a negative charge, and are providing conditions are
right deflected by an electrostatic forces as if they are negatively charged. The scenario leads us
to purpose the question: What are these particles? Are they atoms, ions, molecules or smaller
subdivisions of matter?
Thompson attempts to investigate the situation by classifying its mass to charge ratio. The
brilliance of Thompson shines through as he is able to duplicate his results in two different
versions that yielded the same observational results and similar quantitative results. It is
important to understand that Thompson did not predict what the mass to charge ratio was to be,
only that since these particles were unique and shared similar properties.
Thompson examines the mass to charge ratio via two methods. The first and more complex was
to examine the charge, kinetic energy (via the transfer of thermal energy, which is heat) and the
curvature of the cathode rays in a electric field. The second and less complex was to examine
the deflection of rays in an electrostatic field and magnetic field.
For Thompson’s first series of experiment assumed a bundle of homogenous cathode rays to
begin his experimental investigation. He measured the charge by placing an electrometer inside
the glass tube on the beam of the cathode ray. From this he stated charge was equal to the charge
of each particle multiplied by the number of particles.
Ne = Q
(1)
N = number of particles passing through a cross section of any given beam.
Q = the quantity of electricity (charge) carried by these particles
m = the mass of a dingle particle
e = the charge carried by a single particle
Thompson then examined the changed in temperature an object experienced when cathode rays
collided with the object. He concluded the kinetic energy of the particles was converted into
heat and went on the make the assumption all of the kinetic energy was converted into heat. If
one knows the heat capacity of that object and they can measure the change in temperature, it is
possible determine the kinetic energy (which Thompson noted as W and velocity, v) of the
particles.
½ Nmv2 = W
(2)
Thompson continued, if
magnetic field H, then
is the radius of curvature of the path of these rays in a uniform
mv/e = H
=I
(3)
where I = H for brevity. In replacing N with Q/e one will get the following equations and can
deduce m/e and v by knowing Q, W, and I
(m / 2e) v2 = W / Q
(4)
v = 2W / QI
(5)
m/e = I2Q / 2W
(6)
To measure Q Thompson cleared Hertz tube of the electric field plates and placed an
electrometer inside the inner cylinder and was able to measure Q the quantity of electricity
brought via the cathode rays to the inner cylinder.
Figure 12 Thomson Tube
For the first part of Thomson’s experiment he removed the parallel plates and placed an
electrometer inside. For the second experiment, Thomson utilized the electric field created by
the plates to deflect the cathode rays.
To determine W thin fine strips of copper and iron are placed inside the tube and fastened to a
very fine iron and copper insulated wires that exited the glass tube and traveled through a low
resistance galvanometer. The deflection of the galvanometer provided data to calculate the rise in
temperature of the junction produced by the impact of the cathode rays. Knowing the masses,
specific heat of the metals, and the deflection of the galvanometer one could then calculate the W
or the kinetic energy of the particles in question.
To determine I, in uniform magnetic field that causes the particles to move in a circular path two
large coils placed parallel are placed around the cathode tube. The coils are parallel to each other
and a located a distance equal to the radius of each other away form the tube. The strength of the
magnetic field through the coils is measured by the current passing through them. The curvature
of the cathode rays is determined by relating the chord radius and the height to the segment of
the circle. However Thompson encounter difficult in attaining precision measurements for the
the curvature due to the fact the beam spread across an appreciable distance on the side of the
tube therefore it was difficult to determine the exact location of the beam. Here Thompson noted
that error in his experiment could have been as high as 20%.
Thompson received satisfactory results, in an examination of the tables it is experimentally
observed that the mass to charge ratio is consistent and more importantly independent of the type
of rarified gas. With hydrogen yielding a 0.42 x 10-7 (emu per gram), air 0.40 x 10-7, for
carbonic acid 0.40 x 10-7
Thompson’s second method is based upon the deflection of cathode rays in an electrostatic field.
If you measure the deflection of the cathode rays under a uniform electric field and uniform
magnetic field one can determine the mass to charge ratio assuming the deflection angles are
identical.
First let the space passed over by the rays in a uniform electric field F, be l. The time it takes to
accomplish to travel this space is l/v the velocity in the direction of the force is (Fe / m) (l / v).
F = the electric field
l = the space passed over by the rays in F
The angle,
at which the rays were deflected when they leave the electric field into a neutral
region (free from electric force)
= (Fe / m)(l / v2)
(7)
Instead of an electric field, it is replaced with a magnetic field H, at right angles to the rays, and
traveling across the distance l, the velocity at right angles to the original path of the rays is (Hev /
m) (l / v).
There is a subtle difference between H and, B what is commonly used in today’s introductory
tests. The magnetic fields calculated via Biot-Savat or Ampere’s Law utilize the B field,
measured in Tesla. However when generated field pass through magnetic materials, the
materials themselves produce magnetic fields. It becomes fairly ambiguous what field is created
by the current and what is created by the material itself. What has become known as the
magnetic field strength, defined as the magnetic field from the external current independent of
the magnetic response of the material, measured in amperes/meters. It is determined by the
following equation:
H = B/ o = B/ o – M
(7a)
where M = magnetization of the material
Therefore
the angle at which the rays leave the magnetic field is equal to
= (He / m)(l / v)
(8)
From expressions 7 and 8 we can rearrange the and solve for the velocity and charge to mass
ratio. In order to simplify the calculations further Thompson set = in his experiment and the
following equations arise for the velocity and mass to charge ratio,
v = F/H
(9)
The magnetic field was produced by placing two coils around the tube. The coils are parallel to
each other and a located a distance equal to the radius of each other away form the tube. The
strength of the magnetic field through the coils is measured by the current passing through them.
It was determined by the deflection of a galvanometer with a very narrow wire connected to it.
A current was sent through the outer coils and then reversed the deflection of the galvanometer
was observed. The small coil was placed again between the center of two very large coils so as
to be in the center of a magnetic field and again the current was reversed and the deflection of
the galvanometer was measured. By comparing the ratio the two one could determine the
magnetic field, B.
Figure 13 (a)
(b)
Fig 13a. is a Helmholtz Coil with an circular cathode ray, Thomoson only had a tube large
enough for a partial circle.
13b. A side view of the coil with a magnetic showing the direction of the uniform field at the
middle.
A uniform magnetic field will produce an orthogonal force upon the flow of a electrons causing
the electrons to follow a circle. Knowing the radius and other measure variables it is possible to
calculate the charge to mass ratio of an electron. Let us examine the calculations below:
Knowing the difference in electric potential when passing the electrons through parallel plates
Thomson was able to calculate the velocity for the electrons through energy conservation
eV = 1/2 mv2
(10)
Two wire coils, known as Helmholtz coils are placed a distance apart from each other with
cathode tube at the center. As current flows through the wire it produces a magnetic field on the
flow of electrons inside the tube. The magnetic field forces the electrons into a circular path,
depending on its strength. Since the electrons are traveling in a circle, we can apply Newton’s
second law to centripetal motion
F = mac = mv2 / r
(11)
m: mass of electron; v: velocity of electrons; r: radius of electron path
F = q(v x B)
(12)
Combing the effects of the magnetic field on the electron path, we get
rearranged that is,
mv2 / r = q(v x B)
e/m = 2V / B2r2
(13)
(14)
Know the potential difference between plates, the magnetic field he measured, and he calculated
the radius of the partial circle of electrons. This was accomplished via the relationship between
the chord radius and the height of a segment of a circle Thomson was able to calculate the radius.
See diagram below.
Figure 14: the path of cathode ray being deflected the equation below is a relationship
established between the radius, partial chord and portion of a circle. 2r =CE2 / AC + AC
Thompson then conducted a series of experiments to see if the electrostatic deflection was
proportional to the electric intensity between the plates. The experiment yielded similar
outcomes and was less laborious than the previous. It turns out Thompson values were even
more accurate in comparison with today’s number. He was able to draw two conclusions: (1)
these particles are the same whatever the gas is to create the cathode ray. (2) the mean free paths
depend upon nothing but the density of the medium traversed by these rays.
Thomson’s calculation was the icing on the cake. After stepping up the ladder through each
conceptual jump, he put it all together and calculated m/q. His findings led to Rutherford’s gold
foil experiment and to a better model for the atomic structure of an atom.
Measuring the Fundamental Charge
In his experiments with cathode rays, J. J. Thomson had found evidence for a new
subatomic particle associated with electricity. He had found that the particles composing the
Cathode Ray had a mass to charge ratio different than any other know particles. Michael
Faraday had calculated a value for the charge of a particle involved in electricity and the
ionization of particles. In light of this, Robert Millikan wanted to independently measure the
charge of this particle. He and his graduate student, Harvey Fletcher, calculated it by charging
many particles with only a few charges, measuring the net charge for each particle, and finding
the fundamental charge, e, such that all charges on the droplets were an integer multiples of e.
The effects of air on particles can make it possible to calculate the size of the
tiny particle by analyzing its motion. One can also analyze its motion in air to
find the net external force on the particle. This makes it possible to calculate
the net charge on a tiny particle from experimental observables and known
constants. Millikan and Fletcher built an apparatus that created tiny oil
droplets, charged them with just a few elementary charges, and measured the
droplet’s velocity under the influence of air, gravity, and an electric field.
Since some of the droplets were very small, Millikan had to correct the model
for the motion of particles in air, Stokes’ Law. The experiment concluded that the fundamental
charge had a value of 4.93 * 10-10 electrostatic units, which is comparable with modern
measurements of 4.803*10-10 electrostatic units (1.602*10-19 C).
For particles that air exerts a force one, it is possible to calculate its size from its free fall
velocity, a calculation that cannot be done in a vacuum. Stokes' Law gives the force that air
exerts on a moving sphere.
r
r
F = "6#uav (1)
where a is radius of the particle and v is the average velocity of the particle. If we study the
particle after it reaches its terminal velocity, then Newton’s 2nd Law gives
mg = 6"uav1 .
!
The effective weight of a particle, the actual weight minus the buoyant force of air on the
particle, is
mg = 43 "a 3 (# $ % ) (2)
!
where " is the density of oil and " is the density of air. Combining these two equations, the
radius of the particle can be calculated from its average terminal velocity in free fall and from
other known constants
!
!
a = 2("9uv# $1 )g (3).
!
Assuming that the particle is charged, that an electric field exerts an upward force on it,
and that the particle continues to move downwards, Newton’s 2nd law gives
mg " 6#uav 2
qn =
E
!
And plugging in for m
4 3
"a (# $ % )g $ 6"uav 2
3
! qn =
E
!
where v2 is the average terminal velocity of the particle with both gravity and the electric
field acting on it. Millikan and Fletcher could then compare different values of qn and find a
factor that, when multiplied by an integer, would give qn in each case. This value, they reasoned
would be the fundamental charge.
Millikan and Fletcher built an apparatus that created tiny oil drops, charged them with
just a few electric charges, and measured the observables needed to calculate v1 and v2. Millikan
and Fletcher used oil to create their droplets since it did not
evaporate quickly over time. An atomizer, a device similar to a
commercial perfume sprayer, sprayed small droplets of oil into a
chamber sealed to prevent air drafts. They pumped air into the
chamber through glass wool to cleanse it of dust. In this
chamber, an X-Ray or a radium source ionized the air, helping
to put small charges onto the oil droplets. At the bottom of the
chamber were two circular parallel plates that provided an
electric field. The plates were mounted horizontally a distance
of 1.6 cm vertically apart from each other. A small hole
Figure 2: The Essence of the
through the upper plate allowed oil droplets to fall between the
Millikan Oil Drop Experiment
plates. Two windows directly across from each other
provided light for observing oil droplets between these plates. A third widow 25 degrees away
from the path of the light allowed reflected light to escape the chamber and be collected a
telescope. Using the telescope, they used a stopwatch to measure the elapsed time that it took
the droplet to fall a distance 1.010 cm as demarked by crosshairs on the lens of the telescope and
calibrated by observing a ruler inside the chamber. From this measurement, Millikan and
Fletcher calculated the average speed, v1, of the droplet when acted upon by only the earth.
After turning on the electric field, the scientists measured the elapsed time for the particle to rise
1.010 cm under the influence of gravity and the electric
field, from which they calculated v2. They used a
voltmeter to measure the voltage between the parallel
plates, and hence, assuming the electric field to be
constant, the value of the electric field. Millikan and
Fletcher measured times on the order of tens of seconds.
By turning the E field on and off, the v1 and v2 of the same
droplet could be measured multiple times. Often during
the course of these measurements, the droplet would pick
up or lose a charge.
After comparing the charges on various droplets to
find
the
common factor, the fundamental charge, Millikan
Figure 3: A Diagram of the Setup
observed that the value calculated from measurements on
particles smaller than a certain size were larger than the
values calculated from the rest of the droplets. He hypothesized that Stokes' Law was not
completely accurate for these small particles. Millikan proposed this correction to Stokes’ Law
F = (1+6 "fuav
( l a ))
!
where l is the mean free path of an air molecule at a given temperature and pressure. He
proposed a correction of this form because the correction must diminish as the radius, a,
increases and, judging from his data, it must make the net
force, F, smaller for droplets with a smaller radius, a.
Millikan approximated the correction to be a constant, A,
times l/a. From this equation, he predicted that a plot of e2/3
vs. 1/a would be a straight line. For the initial plot, Millikan
calculated a from the uncorrected version of Stokes’ Law.
Millikan’s measurements confirmed his prediction. From
the slope of this line, a rough value of A could be
calculated. The radius of each droplet was then recalculated
using the corrected version of Stokes' Law. Millikan
created a second e2/3 vs. 1/a plot and obtained a better value
Figure 4: For smaller droplets, the
for A from its slope. This value of A agreed well with
calculations gave a bigger value of the
independent modifications to Stokes’ Law done by
fundamental charge
Warburg, another physicist.
From their analysis, Millikan and Fletcher
determined the fundamental charge to be 4.93 * 10-10
electrostatic units, which is comparable with modern
measurements of 4.803*10-10 electrostatic units.
This work gave scientists not only the charge of the
electron, but also indirectly the mass of an electron. To find
Figure 5: Plotting e2/3 vs 1/a to correct
it, they merely had to multiple the fundamental electric
Stokes’ Law
charge by the mass to charge ratio of an electron that had
been measured by Thomson. This work, along with his
work on the photoelectric effect, was reason for the Royal Swedish Academy of Sciences to
award Millikan the Nobel Prize in Physics for 1923.
Bibliography
Fletcher, Harvey. “My work with Millikan on the oil-drop experiment.” Physics Today
35.6 (1982): 43-7.
Gladstone, Daniel. “Source of the story.” Physics Today 35.6 (1982): 44-5.
Goodstein, David. “In the Case of Robert Andrews Millikan.” American Scientist 89.1
(2001): 54-60.
Millikan, Robert Andrews. The Electron, Its Isolation and Measurement and the
Determination of Some of Its Properties. Jesse DuMond (Ed). University of Chicago
Press, 1966.
Millikan, Robert Andrews. “The Isolation of an Ion, a Precision Measurement of its
Charge, and the Correction of Stokes’ Law.” Physical Review 32(1911): 349.