Download Millikan Oil Drop Introduction Towards the end of the 19th century a

Millikan Oil Drop
Introduction
Towards the end of the 19th century a clear picture of the atom was only beginning to emerge. An
important aspect of this developing picture was the microscopic nature of electric charge. In 1897 J. J.
Thomson demonstrated interactions of “cathode rays” with electrical charge. Thomson proposed that
these rays were composed of small particles (now known as electrons), much lighter than atoms. He
was ultimately able to determine the charge to mass ratio of the the particles in the cathode rays.
In 1909 Robert Millikan devised an ingenious experiment to determine the electronic charge. The
basic layout is illustrated in figure 1. He observed tiny oil drops (created in a fine mist using a device
much like a perfume sprayer) with small amounts of excess charge as they fell and rose in a
controllable uniform electric field. Using rise and fall times, as well as some basic mechanics, he was
able to determine the amount of excess charge on numerous drops. The measured charges were always
integer multiples of a particular value which we now refer to as the electronic charge, e.
Figure 1: Millikan's Apparatus
Oil Drop Physics
The vertical motion of the oil drops follows from Newton's Laws and three basic forces: the weight of
the drop, the air resistance due to the motion of the drop and the electrical force on the drop. The drops
are observed moving under two conditions: falling (when the electric field is turned off) and rising
(when the electric field of appropriate strength and direction are turned on). The equation of motion is
given by
FE=qEy
F y =m a y =q E y −m g−k v y
where the parameters are identified in the following table:
m mass
ay acceleration
q
charge
Ey electric field
g
acceleration of gravity
k
friction coefficient
vy velocity
FG=−
Ff =−kv y
mg
Figure 2: Free Body
Diagram for Oil Drop
Whether falling (under the influence of gravity and friction alone) or rising (under the influence of
gravity, friction and a non-zero electric field), the drops quickly reach their terminal velocity. At
terminal velocity, the acceleration of the drops is zero. The equation of motion can then used to relate
the physical parameters to the falling terminal speed vf and rising terminal speed vr so that:
k v f =m g
and
k v r =q E−m g.
The friction coefficient is determined from Stokes's Law:
k =6  a 
where a is the radius of the oil drop and η is the viscosity of air. The mass of the drop is related to its
size by:
4
3
m=  a 
3
where ρ is the density of the drop. The Electric field is determined from the voltage V applied to the
conducting plates above and below the observation region and the separation d between the plates:
E=
V
.
d
The rising and falling terminal speeds are determined by directly observing the motion of the oil drops
through a microscope. The falling terminal speed then allows a determination of the radius of a
particular drop:
 
9v f
a=
2g 
1
2
.
With the rising terminal speed, charge of a drop can be determined:
q=
k v r m g
E
which can be rewritten as
 
9v f
q=6 
2g 
1
2

v r v f 
.
V /d
Procedure
For this exercise, students will use video analysis of simulation videos to determine the charges on a
number of oil drops. Each clip will contain a number of drops in motion. The each drop's motion
should be analyzed using two separate tracks: one track for the falling motion (with the voltage off) and
one for the rising motion (voltage on). Each data file is labeled md####.avi where the #### represents
a number (from 1 to 6 digits). For each data file there is a text file with the same digits in its filename.
The text file contains ancillary physical data (in MKS units) necessary to complete the analysis of that
video. For example, video file md1702.avi has an associate text file millikan 1702ssng.txt which
contains the following:
rho: 886.000000
eta: 18.240000E-6
g: 9.805000
d: 0.010000
V: 200.000000
tape measure tool
marked drop tracks
player slider
The video analysis program Tracker will be used for this lab. Start Tracker then Video:Import and
select the video clip to be analyzed. Use the tick marks to set the length scale for each video. The
major tick marks are 0.500 mm apart. Select Tracks:tape measure to make sure the tape measure
tool is visible, drag the ends of the tool until the tool is vertical and the length goes from the top to the
bottom major tick marks. Double click on the tools length indicator to set it at .005 (using MKS units).
Play the clip from beginning to end. Depending upon the particular clip, not all drops will rise after the
voltage is turned on. Those oil drops which do not rise may not be suitable for this exercise. Choose an
oil drop to track, use the player slider to set the clip at its beginning, and select Track:New:Point
Mass. Shift click with the cursor carefully aligned with the drops location to mark its position in that
frame. Use the player slider to pick the last frame before the voltage turns on, and mark the drops
location in this frame. If the drop falls briefly out of view, choose the last slide the drop is visible
before the voltage turns on. Another 4 to 6 frames between these two need to be marked to get an
accurate estimate of the drop's falling terminal speed.
Select Window:Right View to open the data window. The default graph is x versus t, so click on the
vertical scale label and choose y to produce a y versus t graph. Right click on the graph and select
Analyze... to open the dataset tool window.
In the Dataset Tool window, select the Fits check box. The default curve fit is linear, which is what is
need for this exercise. The magnitude of the a parameter is the falling terminal velocity; record this
value.
A new track is needed to determine the rising terminal velocity, but the process basically is the same.
Select Track:Mass A and uncheck visible to hide the falling track. Select Track:New:Point Mass.
and use the player slider to pick the first frame after the voltage turns on, and mark the drop's location
in this frame. Use the player slider to determine the last frame that the rising drop is visible (this may
be the very last frame) and mark the oil drop's location on this frame. Again, 4 to 6 additional
markings will be needed between these two frames. Get the y versus t plot of the new track, and use
the Dataset Tool to obtain the rising terminal speed. Note that if you chose a drop that actually keeps
falling after the voltage is turned on (not recommended) you should record the rising terminal speed as
a negative number.
A spreadsheet (millikan.xls) has been set up to facilitate the data analysis. Common parameters are the
plate separation d, the viscosity of air η, the drop density ρ and the local acceleration of gravity g.
Make sure the correct values for your video clips are specified. For each drop, the voltage (which will
be common for all drops in a given clip), the falling terminal speed and the rising terminal speed are
needed in the appropriate spots on in the spreadsheet. The calculation of the drop's radius and net
charge are already set up (you need to show complete sample calculations for your report).
After at least three clips have been analyzed and the charge measurements have been determined, copy
the column of charge values (q) into a separate sheet of the spreadsheet, using the past special −>
values option. Sort the column to see if there is any pattern to the magnitudes of the charges. You
should be able to discern the minimum charge magnitude or the minimum step of in the value clusters,
corresponding to the electronic charge. Use this estimated value of the electronic charge to determine
the integer multiple n of e for each charge value, and make an additional column of the ration q/n for
each charge. Each value of this ratio provides a measurement of e. A sample table of the values
obtained from a single clip is shown below for illustration. Note that this table only contains one clip's
worth of observations, so your data table will be much more extensive.
charge q
1.62559E-19
1.62659E-19
4.88817E-19
9.69274E-19
9.75801E-19
1.14142E-18
1.46199E-18
1.79033E-18
smallest, e?
about 3x smallest
about 6x smallest
about 7x smallest
about 9xsmallest
about 11 times
smallest
multiple e
1
1
3
6
6
7
9
1.79938E-18
1.62559E-19
1.62659E-19
1.62939E-19
1.61546E-19
1.62633E-19
1.6306E-19
1.62444E-19
11
1.62757E-19
11
1.6358E-19
avg e
1.62686E-19
Anomalous Data: As a separate exercise, each group will be assigned to analyze one of the
mdfc####.avi files, determine the values of the charges in their assigned clips and post those values to
the class discussion board. As a result, each individual will analyze and report on all the anomalous
data. Is charge quantized in the anomalous data? Is there any potential explanation for this data from
accepted physics?
Credits:
Figure 1 drawn by Theresa Knott, and obtained from
http://en.wikipedia.org/wiki/Millikan_oil_drop_experiment
Tracker is open source software from Doug Brown
http://www.cabrillo.edu/~dbrown/tracker/