Download Brown University PHYS 0060 Physics Department LAB A

Brown University
Physics Department
PHYS 0060
LAB A - 030
Millikan “Oil Drop” Experiment
References:
1.) Harry F. Meiners et al., Laboratory Physics 2nd ed., Ch. 14, (John Wiley, 1987).
2.) Adrian Melissinos et al., Experiments in Modern Physics 2nd ed., pp. 2-10, (Elsevier, 2003).
3.) X. Zuo et al.,“Making Millikan Movies” Physics Teacher, 46, 365 (2008).
Equipment: Uchida Millikan Apparatus, Latex Sphere Solution, Stopwatch, Flash light or Desk
Lamp, (optional: VideoFlex Camera, Canon Optura 40 Video Camera- to convert Video flex S
video to digital video, Virtual Dub Video Software, Tracker Video Software).
Introduction:
The apparatus shown in the diagram on page 1 of the Uchida Millikan Apparatus manual
is similar in principle to that by which the physicist Robert Millikan, early in the twentieth
century, measured the charge of the electron. We also include information to an older Macalaster
apparatus (no longer available), which contains useful experimental tips that also apply to the
Uchida apparatus. While Millikan used oil droplets in his experiments, we have the advantage of
a modern process for producing latex spheres whose radii are very uniform and known with
accuracy.
The heart of the apparatus is a chamber into which these tiny spheres can be introduced
and their behavior observed. A potential difference can be applied across the chamber, producing
a uniform field within aligned either along or opposite to the gravitational field acting on the
spheres. The spheres acquire charge through ionization so that a force qE, where q is the charge
and E the electric field, may be made to aid or oppose the gravitational force. Using the
apparatus shown, you will be able to observe that the charge on different spheres is quantized —
that it appears as multiples of some unit charge e. This quantum of charge is that of the electron.
Theory:
Effects of the Viscosity of Air — Stokes’ Law
Were it not for the viscosity of air, observation would be quite difficult since the forces in the
experiment would cause accelerated motion throughout. The effect of this viscosity,
characterized by a parameter η, is to produce a force of friction proportional to the velocity v of
the sphere (Stokes’ Law) of magnitude
Viscous force = 6πηvr
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Physics Department
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LAB A - 030
where r is the radius of the sphere. As a preliminary to experiments with this apparatus, you
should consider the motion of a particle acted on by a constant force F (such as mg or qE, or
both) and such a viscous force opposing motion. That is, consider the implication of the equation
of motion
𝑚
𝑑𝑣
𝑑𝑡
= 𝐹 − 𝑘𝑣
In any given observation, we will be dealing with a constant k which is 6πηvr. You should have
no trouble in proving that the particle will attain a constant “terminal” velocity
𝑣𝑇 =
𝐹
𝐹
=
𝑘 6𝜋𝜂𝑟
As a result of this effect, the spheres under observation will be seen to drift at comfortable (i.e.
measurable) steady speeds in the field of the telescope.
Procedure:
Procedure to Verify the Terminal Velocity Effect
Introduce a cloud of spheres into the chamber of the Millikan apparatus by giving the
plastic bottle a sharp squeeze. Focus the telescope on the spheres. They appear to be rising
because the telescope inverts the field of view. Actually the spheres are falling, at various speeds,
under the gravitational force. The field of particles can be thinned out by applying a voltage to
the plates of the chamber, using the switch on the apparatus. The highly charged spheres will
shoot up or down, depending on their charge, and disappear after several reversals of the voltage
switch. When only a few spheres remain in the field, moving slowly under gravity, measure the
velocity of several, one at a time, by clocking them over a fixed scale interval, 10 divisions for
example. The data will probably show that several spheres have the same free fall velocity,
others have approximately double that velocity, and others triple it. This is reasonable evidence
of single spheres, clumps of two, and clumps of three. (Some fragments of spheres may be
observed which are so small that the random Brownian movement bombardment by air
molecules prevents the spheres from falling in a uniform way.)
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Physics Department
PHYS 0060
LAB A - 030
Procedure to Measure the Charge of the Electron
One way to measure the charge of the electron is to cancel out gravitational effects. To do
this for any sphere under observation you will need to observe the terminal velocities first when
the application of the electric field causes the sphere to rise against gravity, and then when the
same field is reversed to aid gravity. In the first case the terminal velocity is
and in the second case it is
𝑣1 =
𝑞𝐸 − 𝑚𝑔
6𝜋𝜂𝑟
𝑣2 =
𝑞𝐸 + 𝑚𝑔
6𝜋𝜂𝑟
Summing these two numbers produces a result which depends only on the charge and not on the
mass. If several observations are made on different spheres in this way, your data should show
the quantum nature of the charge on the spheres, in the groups of nearly equal velocities that are
observed. From the known values of the radius of a single sphere, the viscosity η, and the
applied field E, the charge of the electron may be calculated:
6𝜋𝜂𝑟(𝑣1 + 𝑣2 )
|𝑞 | = �
�
2𝐸
Determine the average value of q for each separate grouping of values of the sum (v1+ v2). The
lowest q should correspond to a single sphere, singly charged. Calculate the ratios of the higher
q’s to the lowest value: all the ratios should be integers, each measured q being a multiple of the
electron charge e.
Compare your determination of e to the accepted value.
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Physics Department
PHYS 0060
LAB A - 030
Sample Student Data: (data taken by eye and stopwatch)
The following student data will give you a rough idea of the typical velocities measured
Plate Voltage = 50 Volts, d=0.005m, 𝜂 =
Trial #
Velocity 1 (m/s)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0.00058
0.00045
0.00038
0.00037
0.00037
0.00036
0.00024
0.00023
0.00023
0.00019
0.00018
0.00015
0.00011
0.0001
0.000046
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1.85×10−4
𝑐𝑚−𝑠𝑒𝑐
𝑔𝑚, 𝑟 = 5.25 × 10−7 𝑚
Velocity 2 (m/s)
0.00036
0.00026
0.0011
0.00037
0.00035
0.00059
0.00009
0.00023
0.00027
0.00018
0.00016
0.00015
0.00012
0.00018
0.00036
| sum of velocities|
(m/s)
0.0094
0.00071
0.0015
0.0074
0.00071
0.00095
0.00033
0.00046
0.0050
0.00037
0.00034
0.00031
0.00023
0.00028
0.000082
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Brown University
Physics Department
PHYS 0060
LAB A - 030
Optional Video Analysis:
Many current research experimental groups use digital video cameras and computer video
software to facilitate their research. Although the human eye is a remarkable optical instrument,
digital video digital technology keeps getting better, cheaper, and easier to use. You can also
make digital videos of your Millikan experiment and save them on the computer/usb drive for
later analysis (See reference 3). The video flex camera (Please check for availability) can be
placed over the telescope eyepiece and adjusted for optimal viewing; the video S image can then
be exported to a digital video camera and converted to a digital video (avi file). You can then
time the sphere’s motion frame by frame with the free/open source Virtual dub (each frame 1/30
sec) or import the video into the Tracker software program and analyze the constant velocity
motion (it should be a straight line whose slope will give you the velocity). Instructions for using
Virtual dub and Tracker are available on the Brown physics 50 and 70 lab wiki at the following
web link
(https://wiki.brown.edu/confluence/download/attachments/2752885/Motion+in+Two+Dimensio
ns_08.pdf?version=4&modificationDate=1386010685000.)
Prelab Videos: Some sample student videos have been made at several plate voltages (200V,
300V, etc.). You can practice trying to get various latex sphere velocities, and do some
preliminary data analysis before coming to lab and actually doing the experiment. This should
hopefully help you with the experiment (See reference 3).
Notes and Questions
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1.
The viscosity of air is a well-measured quantity, available for example in the
Handbook of Chemistry and Physics (Chemical Rubber Corporation).
2.
The equations are given in terms of the electric field in the chamber. What you
measure is the potential difference across the chamber. How are these quantities
related?
3.
Your report should include an estimate of the accuracy with which the electronic
charge has been measured with this apparatus, including all effects you can think
of and how they would contribute to random error in the determination.
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Brown University
Physics Department
PHYS 0060
LAB A - 030
Some additional items about the Millikan experiment
1.) Some parameters for the latex spheres: (These parameters may vary a little, check the
solution bottle where these parameters are listed).
Density = 1.05 gm/milliliter
Diameter of a single sphere = 1.05 microns
2)
A few helpful hints:
a) It will take a little practice to get a satisfactory capture of candidate spheres. The best
results usually occur by shaking the squeeze bottle and then quickly sending a “puff”
across into the chamber. Try not to make a big squirt of liquid into the chamber; however,
all is not lost---the chamber can be easily (but carefully) opened and wiped clean and reassembled. Ask your TA or the technician for guidance the first time.
b) Illumination is important so it pays to spend some time varying the light position and
general alignment to make sure the region where the falling spheres are most likely to be
is well illuminated. The same remark applies for the alignment and positioning of your
telescope.
c) Make sure all optical surfaces are clear and clean (walls of chamber, lenses, etc.).
d) Look at the two items below before you plunge in.
3)
There are several ways to approach the experiment and its analysis depending upon the
apparatus. On the next few pages are described some typical approaches which may
provide you with some ideas on how to proceed.
a) Some comments about analysis of experiments done with the Uchida apparatus.
b)
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A reprint from the Melissinos book using different apparatus but with a variation
on analysis which some of you might want to try.
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Brown University
Physics Department
PHYS 0060
LAB A - 030
COMMENTS ON ANALYSIS USING THE UCHIDA APPARATUS
First of all you might note that the fact that charge on the electron is actually quantized can be
found even when there are two quantities which you need never measure separately in this expt.
They are the radius (or mass) and the attached charge of the individual drops. That is because the
terminal velocity depends upon both - and as your write up explained. The little latex spheres,
each one almost precisely 1/1000 mm (from the write-up), more often than not stick together and
so your sample has many different masses as well as “effective radii” and so you can never know
the true radius to use in the Stokes law expression. However, there is a nice way to re-group your
data so that all the ones of the same “effective radius” can be treated together. That is because
that group will all have the same mass and in your “no-field” runs all their drift velocities will
cluster around a similar value. Now, within each of these mass groups there can be the full range
of numbers of electronic charges that have attached themselves and therefore contribute to the
different resulting drift velocity for + versus - electric field. So how does one proceed? If you
look at your functional relationship among all the variables, you will recall it gave the total
charge Q on a drop of radius R as:
𝑄=
6𝜋𝜂𝑅(𝑣1 + 𝑣2 )
2𝐸
But since we can never simultaneously measure Q and R (effective) on a single object and we
can make a grouping of droplets of the same mass (and R) by looking at their no—field drift
velocity, we should instead form the ratio of Q to R:
6𝜋𝜂
𝑄
=�
� (𝑣1 + 𝑣2 )
2𝐸
𝑅
the viscosity, η, is known(∼1.85E-4 gm/cm-sec) and the quantity (v1 + v2) you get from your
data. (Incidentally, the scale in the telescope and the image on the space it is in focus on are
always at the same relative position and so it matters not if you move it around. Also in order to
get the absolute calibration in mm or meters you can just look through the telescope at a ruler or
other scale you have handy-you would find that 15 divisions gives ∼3 mm depending on your
telescope type.)
So now what? Well we can plot a bar graph of all our no-field data and see how they group. You
can either plot the times drifted over the same distance (say 10 divisions) or the actual velocities.
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Physics Department
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Lets say that you plot the drift time for 10 div. and I find 3 distinct groups around 30sec, 60sec,
90sec. You can then, separately for each group and each droplet, calculate the Q/R from their
(v1+ v2)’s. Within each group, they will not turn out to give the same value of Q/R however.
Why? Because they do not necessarily all have the same number of charges on them. In fact, we
should hope they don’t otherwise we can never find the smallest charge they could carry (that is,
1e) as the next step should show.
Now we have the Q/R for each drop in the 30, 60 and 90 groups. In each group pick one
droplet’s Q/R and divide all the other Q/R’s by it-that way, we eliminate the unknown R from
that sample and have just the ratio of the charges on the drops. And the ratios should cluster
around the ratios of small, whole numbers because we expect them to just be different integer
values of e. For example, suppose the one you chose to divide all the others by had 2e on it and
the others had various amounts like 1, 3, 4, 6. Then you would expect your results to be 1/2, 3/2,
4/2, 6/2.
So you get these “fractions” from the 30, 60 and 90 data separately and now you can manipulate
them in various ways-separately and together (for example, try choosing different droplet to
divide all through by; like the one that gives the largest fractions) to see if you can (a) deduce
that charge is indeed quantized and (b) what is the smallest quantity of charge you have
observed. In spite of the simplicity of the apparatus, it is a very powerful experiment if you try to
think carefully what it is you are really trying to measure and use care and patience. Millikan
didn’t win the Nobel Prize because it was easy. It also helps to plot the data as you go along to
reveal trends, problems and sometimes to suggest solutions.
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