Download Lab 1: Millikan`s Oil Drop Experiment

Physics 128
Fall 2003
Lab 1: Millikan’s Oil Drop Experiment
Be sure and finish the pre-lab assignment before coming to lab.
Introduction
The oil drop experiment is one of the most important experiments in modern physics. Robert Millikan
(American: 1868-1953) perfected and performed his oil drop measurements during the period 1909 – 1915.
In 1923 he was awarded the Nobel Prize in physics for his measurement of the electron charge and
verification of Einstein's theory of the photoelectric effect. In this lab, we will fairly accurately reproduce
his determination of the fundamental unit of charge by observing the motion of extremely small oil drops
under the influence of three forces: gravity, viscosity (air resistance), and an electric field.
Safety Note:
This experiment will include the use of a γ−ray source. It can be a hazard if improperly handled, but is safe
if treated properly. In this respect, it is no different from any other lab equipment. Simple precautions will
keep the exposure during the course of the lab well below NRC limits (actually below the normal
background level in some areas of the US. There are three simple ways to limit radiation exposure:
distance, time, and shielding.
Radiation obeys the inverse-square intensity law. Keep sources a reasonable distance from yourself and
other lab participants. The exposure from a source at two inches is 144 times as great as the exposure at
two feet! Handling sources should be done economically. Unnecessary contact should be avoided. The
less time one spends near a source, the less exposure one receives. But when handling a source, do it
carefully and conscientiously. When a source is used for an extended period of time, it will be shielded.
Apparatus:
The apparatus is sketched in your textbook (p. 109). It consists of a set of parallel plates to which a high
voltage power supply has been attached. A small hole in the upper plate allows us to spray a very fine mist
of oil into the plates. When sprayed into the plates, a very few of the oil drops become ionized and hence
respond to the electric force created by applying a voltage to the plates. By timing the motion of the
movement of the drops between a known distance, we can determine their terminal velocity.
Measurements of the terminal velocity under free-fall and with a voltage applied to the plates will allow us
to determine the electric charge of the oil drop. Please read section 3.11 in you book carefully before you
come to lab.
Experiment:
1. With the help of your instructor, familiarize yourself with the equipment.
2. Begin by noting the time and the voltage on the plates.
3. Prime the atomizer by pumping the bulb several times until you get a good mist (directed at a shield).
Open the port and spray a squirt into the chamber. Close the port.
4. Make your measurements on an oil drop. I recommend using a drop that falls through the standard
distance l in a minute or less. (Remember to put your data down in a neat and orderly way so that
later you will be able to understand exactly what you did.)
• Time the drop as it fall under the forces of gravity and viscosity alone → tg.
• Then time the drop with an electric field applied to move the drop upward → tu.
• Then time it with an electric field applied to move the drop downward → td.
(When you are applying the field, please note the direction of the field because later you may find
that the charge on the drop changes sign.)
• Repeat the measurements with the electric field on a few times so that you can build up some data,
take the average, and minimize your uncertainty in this measurement.
• Bring the drop to the top and expose the drop to the radioactive source while you time it in free
fall (no electric field) again. Then time the drop with an electric field applied to move the drop
upward or downward. If the time is significantly different from what you measured previously,
make a few more measurements with the electric up and down as before. If not, bring the drop to
the top, time it as it drops again while exposing it to the radioactive source. Soon enough the
charge will change.
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Physics 128
•
Fall 2003
Make your table as neat as possible. You may want to follow the format below:
tg (s)
96.64
δt g (s)
0.05
Exposed To Radiation
96.57
0.05
96.48
0.05
96.55
0.05
•
•
tu (s)
13.47
13.52
13.44
δtu (s)
0.05
0.05
0.1
td (s)
10.60
10.58
10.62
δtd (s)
0.05
0.05
0.05
6.30
6.41
0.05
5.54
0.05
0.05
5.55
0.05
Etc.
Gather as much data on that drop as possible, hopefully getting a number of measurements with
the drop in number of different charged states.
Note the voltage at the end again.
Analysis:
Classical fluid mechanics tells us that the terminal velocity of a small sphere subjected to a force F is
F
, where r is the sphere radius and η the viscosity of the gas in which the sphere moves. If the
6πrη
4 3
only force was due to gravity then we would have F = Mg = πr ρg , where ρ is the density of the
3
2 r 2 ρg
. In the Millikan oil drop
oil drop. The terminal velocity of the falling oil drop is therefore v =
9η
experiment one knows the values for ρ , g , and η . By measuring v one can calculater and then M .
v=
We will conduct the Millikan oil drop experiment in the presence of an applied electric field. The electric
field’s direction can be switched. Hence, we can either force to particle to move upwards, or increase its
velocity downwards.
1. Collect your free fall (gravity and viscosity alone) timings. Use these to determine the radius of the
particle using the following equation (which you should be able to derive):
 9lη
r =
 2 ρgt
g

2.
12

 .


Remember to propagate the uncertainties through and include an uncertainty in your final value.
Now prove to yourself that the expressions for the magnitudes of the terminal velocities down and up
are given respectively by
qE + mg
qE − mg
and
.
vd =
vu =
6πrη
6πrη
Prove to yourself that
1
1
qV
+
=
= Kq .
t d t u 3πrηld
You should find that your measurements are clustered about more or less equally spaced values and are
an integer multiple of some basic unit. Since K is a known quantity (determined from known
quantities and the radius you just indirectly measured) this suggests that q=ne where e is a fundamental
unit of charge, where n is an integer .
•
Guess what the correct values of n should be for each of your measurements.
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Physics 128
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Fall 2003
Make a graph of 1/td + 1/tu vs. n. You should find that the points fall on a straight line and from
the slope of this line (and your determination of K) you should be able to determine the
fundamental unit of charge.
The uncertainties in the values in the table below are probably around 1% or so. You should pay
close attention to your uncertainties and your final value for the fundamental unit of charge
should indicate your confidence in the number (expressed with a ± …). If you need some
review of uncertainty propagation, consult your lab instructors.
Here's some useful data.
Symbol
l
ρ
d
η
Quantity
Timing distance
Density of oil
Distance between plates
Viscosity of air at 20°C
Value
1.71 x 10-3 m
0.876 x 103 kg/m3
0.831 x 10-2 m
1.82 x 10-5 N·s/m2
Required Work:
After you finish your analysis, show your lab notebook to an instructor and they can talk about the
experiment and your analysis. They will give you some feedback on your work and give you some
indication as to how they think you’re doing (e.g. “great job and thorough understanding demonstrated”, or
“good work and fine understanding”, or “you need to spend some more time thinking about this
experiment”).
Be prepared to answer the following questions.
• Why do we believe electric charge comes in fundamental units?
• How does the oil drop become charged? How do you know?
• How did you determine the uncertainty in your measurement?
• What are the principal uncertainties in this experiment?
• How did determine which n to use in your graph?
• How does changing the voltage affect the terminal velocities?
For this lab’s assignment you need to write a proper abstract for the experiment. Please refer to the Lab
Report Handout for further details. Your abstract will be due at the beginning of the next lab. You
instructor may ask you questions about you experiment as well.
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