Experiment 3: The Charge of the Electron
There is an electronic answer sheet (an Excel spreadsheet) in the lab's computers rather than a
printed one. You will print it when the experiment is complete.
The experiment is to measure the electron's charge using a version of Robert Millikan's oil drop
experiment. (He was the first to measure e, in 1909.) Small drops of oil are sprayed into the space
between two charged metal plates in a brightly lit chamber. Seen through a microscope, it is much
like watching dust motes floating in a beam of sunlight. You select one to watch. Rubbing against
the sprayer gives it a small electric charge, which you determine by how fast it moves: How fast
the drop falls with the electric field off tells you its weight. (The faster it falls, the heavier it is.)
The weight and how fast it rises with the field on tells you the charge on the drop. (The faster a
given amount of weight rises, the larger the charge on it.)
You repeat this, determining the charge on many drops. Anticipate spending much of the period
gathering data. Each drop gains or loses a whole number of electrons, so its charge is a multiple
of e. Your results, therefore, should clump up around charges of e, 2e, 3e, 4e, etc., allowing you
to determine e.
Procedure:
1. Take the lid off the chamber, then tip its contents into your hand. Measure the thickness of the
plastic spacer between the upper and lower plates with a micrometer. Just record it in the margin
of this page. When you reassemble, the hole in the black plastic part goes on the bottom.
2. Set things up and notice some controls:
a. Mount the apparatus on a ring stand at a convenient height. There is a level on the
apparatus, but this doesn’t have to be perfect. Shim the ring stand’s corners if it’s way off.
b. Plug the “plate voltage” connectors into
250 V and 0 V on the power supply. Also
connect a meter set for 0 – 1000 DC volts
there. Leave the thermistor connectors empty.
c. The lamp’s 12 V power cord plugs in near
the level. The knob on top of the lamp adjusts
its horizontal position and the knob by the power cord adjusts its vertical position. These are
probably correctly adjusted. Leave them alone unless there is a problem. Try the focus first.
d. There are two focus adjustments on the microscope: The ring around it near the eyepiece
focuses on the reticule, the marks imposed on the field of view. You probably won’t need to
use this. The one at the end by the chamber focuses the oil drops. Since different drops can
be at different distances, you will probably readjust this several times.
3. On the computer, open Excel. Open the file called millikan, where most of the calculations are
already set up. Do not type anything over the formulas in columns M through S.
4. Turn on the light (by plugging it in), meter and power supply. Read the voltage. From this and
the separation of the plates, calculate the electric field in the chamber. (In a uniform field, ΔV =
Es.) Enter this and copy it all the way down column B; it will not change between trials.
5. Put the 3-way switch (on the end of the cord) in its center position, turning the field off. Put the
lever on the side of the chamber in its center position: “Spray Droplet.” Darken the room. Put the
tip of the sprayer in the hole on top of the chamber. It will be tipped at something like a 45° angle.
Look into the microscope and squeeze the bulb once or twice. You should see little dots of light
like faint stars. These are the oil drops. Adjust the focus if necessary.
6. Move the lever by the chamber toward you to “Ionization Source Off.” This closes the opening
through which the drops entered.
7. Move the 3-way switch to turn on the electric field. It doesn’t matter which way you move it
because some of the drops are positive and some are negative. Look for a drop which rises fairly
slowly, since these have the smallest amount of charge. If you can’t find one you like with the
field pointing one way, try it the other way. If necessary, spray in more drops.
8. With a stopwatch, measure the time for your drop to rise one large division (5 small divisions)
with the field on. Also measure the time for the same drop to fall one large division with the field
off. (Not reversed, OFF. Switch in the center position.) Enter these under the headings u1 and
d1. (U for up, d for down.) The spreadsheet will immediately tell you the charge on the droplet.
9. The uncertainty in anything over 7 x 10-19C is too large. If q is more than this, discard the result
and try another drop. Otherwise, repeat the time measurements several times – five if possible.
(They can vary more than you might think.) The spreadsheet will average them. If the drop moves
quickly, measure the time for several divisions and divide. The number on the stopwatch before
dividing should never be less than ten seconds.
To repeat: Time it going up once and down once. Don’t waste more time on that drop if it is over
7 x 10-19C. Pick a new drop and write over the old data. But if it is under 7 x 10-19C, time it going
up and down several more times for better accuracy. Don’t take your eye off the drop unless
you are certain you can find the same one again. Have someone else read and record the
time. If the drop gets too close to the top or bottom, move it back by reversing the field. When
finished, write down the charge or back up to a flash drive as a precaution. Try not to spend more
than 8 or 10 minutes on each drop.
10. Repeat with other drops until there is a clear pattern or 40 minutes before the end of the period,
whichever is first. You may not need all 18 rows on the spreadsheet.
11. When finished, set up a histogram to display the results. The histogram divides the x axis into
pieces called “bins” and shows how many data points are in each bin.
Click “Data” at the top of the screen.
Click “Data Analysis” at the right.
Highlight
“Histogram” then click ok. Click in the “Input Range” box, and then highlight the cells
containing results in the charge column. Click in the “Bin Range” box, and then highlight all
of the occupied cells in column S. Click in the “Output Range” box and then click in cell
A20. Check “Chart Output.” Click ok. Enlarge the histogram if necessary to make it easier
to read, and drag it to a convenient place.
If all has gone well, your data will fall into clumps, at multiples
of e. Find the average charge of each clump. Some clumps
might be missing, and you might also have some inaccurate
points scattered around. It's ok as long as you have enough good
results to spot the pattern. If not, ask the instructor, but you will
probably have to go back for more data if time permits.
12. When you have enough data, print. Print only page 1.
13. Average the values for e based on each clump, (e, 2e/2, 3e/3, etc.) and compare to the accepted
value. Don't bother calculating an uncertainty. If this works at all, you should be within just a few
percent of the accepted value.
The Calculations:
Just because the spreadsheet was already set up doesn’t mean you don’t have to understand what it
did. I will be looking for a summary of this when I read your discussion.
Include how you found the electric field, E, including the numbers you used.
The speeds: One large division is .0005 m. The speeds are (that distance) ÷ time.
The drop’s weight in newtons: You can tell something’s weight from its terminal velocity, in
column I, because heavy things fall faster. A skydiver falls faster than an ant, for example. (The
formula is based on a relationship called Stokes’ law, with a correction for the fact that the drops
are no larger than the mean free path of the air molecules. The constants depend on atmospheric
pressure, the viscosity of the air and the density of the oil.)
The drop’s charge: The diagrams show the forces on a drop as
it rises or falls. In both cases, the speed is constant so ΣF = 0.
(The drop reaches a terminal velocity almost immediately.)
Except at much higher speeds, friction from a viscous medium
is proportional to speed, f = kv. vu is the speed when going up;
vd is the speed when going down. In your report, write two
equations based on ΣF = 0, one for each picture. Solve the
falling drop's equation for k. Use this substitution to eliminate k from the other equation, and solve
it for q. Notice that everything in this equation was determined in previous columns.
When you finish, please shut down the computer.