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Kirsten Strandjord
Modern Physics 281
The Millikan Oil Drop Lab: Showing the Quantization of charge.
Abstract:
We constructed an experiment similar to the Millikan Oil Drop Experiment to
measure the charge of an electron. We did this using an electric field and a gravitational
field, and using charged plastic spheres, instead of oil droplets. We put these spheres in
viscous fluid and observe the electrons in earth’s gravitational field. We determine the
force of the fluid and that will equal the force of gravity. From here we find the mass of
the sphere or spheres. We apply an electrical force and this will send the sphere in the
opposite direction of gravity. Therefore, the electrical force will equal the gravitational
force added to the force of the fluid. Then we can find the charge. The purpose and
importance of this lab is widespread and applies to all nuclear physics. It is also very
important in showing that charge is quantized value instead of a continuous value.
Introduction:
Robert A. Millikan made several discoveries in the fields of electricity, optics,
and molecular physics. One of his most accomplished experiments was the “falling-drop
method”, which accurately decided the characteristics of a charge-carrying unit, the
electron. 1 Millikan first performed the Millikan Oil Drop Experiment with the assistance
of Harvey Fletcher. In 1913 he published the results of his studies.2 Like in our replicated
experiment he used two metal electrodes and gravity to measure an elementary charge.
He used drops of oil (which is where our experiment deviates) and determined the
common charge to be 1.592 x 10-19 Coulombs.
In our experiment we used plastic charged spheres instead of oil droplets, only in
order to simplify the procedure. When the electric field is turned off the spheres are only
under the forces of gravity and the force of the viscous fluid. The terminal velocity of the
spheres is reached quite quickly. When a voltage is applied to the electrical plates (that
are .5cm apart) the plastic spheres can be manipulated by the forces of the electric field to
move up and down between the plates. Again, the terminal velocity is met almost
immediately. There is a microscope for the experimenter to observe the rise and fall of
the spheres. There are lines spaced .5mm apart in which the observer can then calculate
the distance traveled and measure the time in which the sphere takes to travel. Then the
velocity of the sphere can be calculated. The velocity is an important measurement when
it comes to finding both the mass and the charge.
We would expect significant error when conducting this lab with the apparatuses
that we use. The Millikan oil drop experiment has been enhanced from the original
procedure. Microscope calibration and plate separation are large components of
experimental error. Using a computer opposed to the stopwatch could reduce our error.
The computer acts as a “smart” stopwatch. This also eliminates the “guess work”
associated with measuring the distances with just the experimenter’s eye. 3
Experiment:
To begin the experiment we spray charged plastic spheres in between the plates
and observe through the microscope. The spheres appear as tiny points of light in a clear
viscous fluid. We watch as the spheres fall. Since the view through the microscope is
inverted, the spheres actually appear to rise when they are falling. For clarity’s sake, we
will continue to call this “falling.” We choose any sphere to observe, and measure the
time it takes for the sphere to fall. We do this by measuring the time(s) with a stopwatch
and measure the distance in between the lines that are .5mm apart. We vary our trials by
measuring different distance segments; we use .5mm distances, 1mm distances, and
1.5mm distances. We do this for three different spheres a total of 25 different times.
Since we calculated the distance traveled and the time it takes to travel, from here we can
calculate the velocity at which the sphere travels. Once we know the velocity of the
sphere under only these two forces we can determine the mass of the sphere using this
relationship of forces (also, see picture1):
Fg= ma
Fv= 6adown
Fg = Fv
mg = 6adown
where: m is the mass of the sphere that is to be determined
g is the acceleration due to gravity (9.8 m/s2)
a is the radius of the sphere (5 x 10-7m)
 is the viscosity of air1.82 x 10-5pascal seconds.
down is the velocity that we calculated.
Picture1 Displayed to
the right is the
diagram of forces
when there is only the
force of gravity and
the force of the viscous
fluid applied to the
sphere.
Fv
Fg
Now that we know the mass of the sphere, we can find the radius by knowing
m=
4
 a3
3
where:  is the density of latex (1.05 x 103kg/m)
We create an electric field by putting a voltage on each plate and creating a
potential difference of 200V. We watch as the spheres rise. Again, since our view
through the microscope is inverted, the spheres actually appear to fall when they are
rising. For clarity’s sake, we will continue to call this “rising.”
We choose any sphere to observe, and measure the time it takes for the sphere to rise.
Once again, we do this by measuring the time(s) with a stopwatch and measure the
distance in between the lines. We vary our trials by measuring different distance
segments; we use .5mm distances, 1mm distances, and 1.5mm distances. We do this for
three different spheres a total of 25 different times. We can calculate the velocity at
which the sphere travels.
The electric field has applied an additional force to the sphere. We can determine
the charge of the sphere using this relationship of forces (also, see picture2):
FE= qE
FE= Fg+ Fv
qE=mg +6aup
Picture2 Displayed to
the right is the
diagram of forces
when there is the force
of gravity, the force of
the viscous fluid, and
the electric force
applied to the sphere.
FE
Fg+ Fv
Knowing the relationship between the electric field(E), the voltage(V), and the
distance between the plates(D), we can solve for our charge(q).
q = 6a(up+down)D/V
Using these various equations and our experimental data we can determine the
charge associated with each of the charged plastic spheres. When we divide the charge of
our spheres by the charge of an electron (1.60217646 × 10-19 coulombs), if the values are
integer values or close to integer values we can say that charge is quantized. This means
that that charge comes in “chunks” instead of continuously.
Once we determine whether the data shows quantization of charge, we will use
our “best” data (i.e. most consistent integer within the sets of data of spheres) to
determine the charge of an electron. For instance, if we find that the number of electrons
for one sphere falls closely to 12, we will divide each charge found by 12 and then make
a histogram of those values.
Results and Discussion:
When we applied the equations that were previously derived, we found that our
average calculation for the radius of each of the three spheres is:
r(sphere 1)= 5.2313 × 10-7m
r(sphere 2)= 5.3999 × 10-7m
r(sphere 3)= 5.3228 × 10-7m
For the first sphere, we found that when we divided the charge by the charge of an
electron and made a histogram of our data, that the number of electrons first fell around
the integer 9. As time went on, some of the charge must have dispersed and fell off the
charged sphere. The integer value then went from 9 to 6, from 6 to 5, and then from 5 to
4. This would still conclude that charge is quantized, but it would mean that the charge
was changing as the sphere traveled through the viscous fluid. The friction caused by the
viscous fluid can affect the charge lost by the sphere. Since it is possible that the sphere
might lose charge, but it still loses charges in integer values, the data still show
quantization of charge. The standard error for these values is .73944.
Charge(C) for Sphere 1/ e
Charge of 1st Sphere / Charge of e
1.2
1
Count
0.8
0.6
0.4
0.2
0
3
4
5
6
7
8
Charge/charge of an electron
9
10
For the second sphere, we found that when we divided the charge by the charge of
an electron and made a histogram, the data gave us an integer value tending towards 12.
There were a few outliers in our histogram; including a value near the integer 14 and the
integer 5. Since we only recorded a few of these values overall, I would assume that they
are some form of error, and that they do not correlate with what we would expect.
Overall, from this data it still appears that charge is quantized. Most of our values
fall closely to the integer value 12, and the other values fall closely to integer values. The
standard error for this set of data is .80465.
Charge(c) for sphere 2/ e
Charge of 2nd Sphere / Charge of e
2.5
2
Count
1.5
1
0.5
0
4
6
8
10
12
Charge/charge of an electron
14
16
For the third sphere we took far less data than we did for the previous two
spheres. This could explain why our data does not fit what one would expect when
looking for the quantization of charge. Although most of our values are very close to one
another and the standard error is very small, the values are not extremely close to integer
values. We should have had a better representation of quantization. The standard error for
this set of data is .040493.
Charge for sphere 3 /e
Charge of 3rd Sphere / Charge of e
1.2
1
Count
0.8
0.6
0.4
0.2
0
3.5
3.55
3.6
3.65
3.7
Charge/ charge of electron
3.75
3.8
To find the charge of an electron, we will use the data taken from the second
sphere. We found earlier from the “charge of sphere 2/ charge of e” histogram that the
number of electrons was most likely 12. We take the charge data from sphere 3 and
divide it by 12. We make the histogram below. From our table of values, we find that the
estimated value for e- is 1.5629 x 10-19 Coulombs. The standard error for this found value
is 1.0742. This makes the range of our value for e 1.45548 x 10-19 Coulombs to
1.67032x10-19 Coulombs. Expected charge of an electron fits within this range. The
expected charge of an electron is 1.60218 x10-19 Coulombs.
estimated value of e-
Charge of an Electron
2.5
2
Count
1.5
1
0.5
0
-20
6 10
8 10
-20
1 10
-19
-19
1.2 10
-19
1.4 10
Charge (Coulombs)
-19
1.6 10
-19
1.8 10
2 10
-19
Conclusion:
In our replication of the Millikan Oil Drop Experiment, we sufficiently measure
the charge of an electron. We do this by using force relationships and by substituting in
variables for these different forces. We also demonstrate with this lab that charge is
quantized. Charge is restricted to discrete values, and is not continuous. Charge has the
nature that it comes in “chunks.” As expected, each sphere has a different number of
“chunks” or electrons.
When we observe the “falling” of the spheres, we view two opposite forces acting
upon the sphere. Since the terminal velocity is met almost immediately, the velocity can
be considered constant and the average velocity down satisfies the purposes of our
experiment. Using these values for velocity (v) and substituting other known variables
into the equations previously stated, the radii of the spheres are found. Averaging the
values of for the radii we find that the radii of the spheres 1, 2, and 3 are 5.2313 × 10-7m,
5.3999 × 10-7m, 5.3228 × 10-7m; respectively. We use these values for each sphere in
later calculations.
When we observe the “rising” of the spheres, once the electric field is applied, we
view three forces acting upon the sphere. The force of the electric field is in the upward
direction, and the force of gravity and the force of the viscous fluid act in the opposite
direction. Again, we can use the average velocity for the purposes of our experiment, and
we calculate the velocity upwards. Once we know the velocity upwards and downward
we can apply this to our sum of forces equations previously stated and determine a charge
for the sphere. We divide by the charge of an electron (1.602 × 10-19C) for each of the
values we find for the charge of the spheres. For the first sphere we find that, although
our data fits with the concept of quantization, we cannot determine an actual number of
electrons for sphere 1. It seems as though the friction of the viscous fluid is stripping the
sphere of its charge. It’s still losing charge in increments of charge of an electron. This is
cohesive with the theory of quantization. For the second sphere we find that the number
of electrons is most likely 12. Not much can be determined from our third sphere, except
that more data should have been taken and there may have been error within our
apparatuses. The error could be specific to faulty stopwatch operating, or it may have
been due to discrepancies in the viscosity of air, or the density of latex (i.e. although the
density of latex was correct for other spheres, perhaps this specific sphere had a different
density… etc.). It would have been best to have more trials for the third sphere.
When determining the experimental charge of an electron, we took the most
consistent data (from our second sphere), and since the data suggested that the number of
electrons was 12, we divided each of our values by 12. This gave us a value of the charge
of an electron to be from 1.45548 x 10-19 Coulombs to 1.67032x10-19 Coulombs. This
range is with our error worked in. This range includes what is scientifically accepted as
the charge of an electron (1.60218 x10-19 C.)
From the findings of this lab, we conclude that charge is indeed quantized, and
that the charge of an electron falls within the range we found experimentally. As Millikan
had already displayed, charge comes in “chunks” and these “chunks” have specific
charge values known as electrons.
References:
1
“Robert A. Millikan: The Nobel Prize in Physics 1923,” Les Prix Nobel (1965).
From Nobel Lectures, Physics 1922-1941, Elsevier Publishing Company, Amsterdam,
1965
2
“Oil-Drop Experiment”, http://en.wikipedia.org/wiki/Oil-drop_experiment, October 10, 2008.
3
“The Millikan oil-drop experiment: Making it worthwhile” American Journal of Physics
Volume 63, Issue 11, pp. 970-977 (November 1995 .)