This
is a very much abbreviated (and occasionally facetious) example of what a
report should contain. It is given as a guide and is not intended to be a full
report. Commentary is written in italics. There are several places where
an actual report would include further discussion, further data, further
analysis, etc. Also inserted are a few examples of what NOT to write. As you get more sophisticated and go on to
more research-oriented experiments, you should consult the style of Physical Review
or Physical Review Letters. Pick an article you like, and try to imitate
the style.
About the honor code and plagiarism: You may quote from any
source if you place the quote “within quotation marks” and cite the reference.
You may use figures from any source if you explicitly cite the reference in the
caption to the figure. You may NOT include ANY FIGURES OR TEXT from books or
the web or the laboratory writeup without citing the
exact reference. All text not enclosed within quotation marks must be written
BY YOU. All figures not explicitly attributed to some external source must be
constructed BY YOU. You may discuss the experiment with anyone you wish, and
you may include tables of data and calculations which you did in cooperation
with your laboratory partners (but not from reports of previous years!). You
must prepare and write your own report. Never cut and paste from another
student’s report or from the web.
The Millikan Oil Drop Experiment
R.J.Doe
Phys 506 , Dept. of Physics, KSU
Abstract
Be brief: state the conceptual goal of the
experiment, the approach, the result and the conclusion. The purpose of an
abstract is to provide enough information to the reader that he or she can
decide whether to read the rest of the article.
We used the classical method of Millikan to measure the charge of the electron. Small charged oil droplets were observed to move with constant velocities under the influence of gravity and of applied electric fields of known values. From the measured velocities of the droplets, the charge on each drop was deduced. From the resulting charges a common quantum of charge was found. The resulting value for the electronic charge was found to be (1.53 +/- .2) x 10 -19 C, lower than the accepted value of 1.6 x 10 -19 C by 9.5 %. We conclude that the electronic charge has changed its value over the past hundred years.
Introduction
The introduction
should be abstract, not concrete: describe the background of the experiment and
possibly the principle of its operation. Do not include concrete details about
the structure of the apparatus, the temperature of the room, etc. For example,
do not write: “The apparatus was set up in the corner of the room. It was
connected to a 300 V power supply, and to an intense light. We took twenty
readings for different conditions, 10 by Sam and 10 by me. We used a voltage
meter to get the voltage we used an electronic clock for timing. “
The discovery that electrical charge is quantized was one of the first indicators that matter is made up of charged particles, each of which bears a well-defined charge. Today all known constituents of matter which appear as free particles, including not only the stable electron and proton, but also all “elementary particles” are known to possess charge which is a multiple of this quantum. Determination of the fundamental quantum of charge was first carried out by Millikan [1] in 1607. His approach was to measure the charge on the electron by measuring the charges on small droplets of oil produced by atomizing oil in a simple sprayer. The charges so obtained were found to be integral multiples of a single quantum, from which he could deduce the value of this quantum. While this basic method has today been supplemented by numerous other approaches to obtaining this value, it remains a classic method not only because of its simplicity but also because the resulting charge is independent of the knowledge of other natural constants. So classic is the approach that, even within the last two decades, it has been used to seek fractionally charged particles such as would result from the existence of free quarks in the physical world.
Since Millikan’s experiments were
carried out by undergraduates at a relatively unknown institution (Caltech),
one must question whether these students really knew what they were doing at
that time. Thus the original experiments demand renewed examination.
Furthermore, there has been considerable question raised in recent years as to
whether the constants of
Experimental Approach
In this section you
should start with a conceptual description of how the experiment works before
you go into concrete detail, unless you already covered the principle of the experiment in the
introduction. Do not begin this section with “The density of the oil was 0.89
gm/cm2. We first grounded the cable to the wall socket and then connected the
high voltage lead to the lower plate. We adjusted the light and took measurements . “
The charge on small droplets was determined by measuring the
velocity with which small oil droplets fell (or rose) in air, with and without
the application of an electric field of known value. Using
The basic apparatus is shown in figure 1.
Fig.1. Schematic of apparatus.
Small oil droplets were produced by spaying a fine mist of oil into a pre-chamber, from which they drift into a smaller chamber located between the plates of a parallel plate capacitor. This region was illuminated by a strong lamp and can be viewed by a magnifying telescope where the forward scattering of light by the droplets provides a clear image of them against a dark background. The capacitor plates were attached to a DC power supply to which voltages up to +/- 300 V can be applied. The plates were separated by 0.8 cm.
Charged droplets were isolated by manipulating the applied electric field to retain only the charged ones within the field of view. Using a calibrated reticule mounted within the telescope, the times required for these droplets to move a known distance were recorded under three conditions: field-up, field-free, and field-down. From these times, values of the corresponding velocities, denoted v+, vo and v_ were deduced. The velocity set was measured at least ten times for each droplet, and the average value was used in the calculation.
And so forth.. Explain how you calibrated the reticule, how you did the
timing, etc. It is often a good idea to break a section into sub-sections with
specific headings.
Data analysis
In this section you
give details. Just describe it clearly enough that another student could be
expected to be able to read it and understand it, without having read the
laboratory writeup. The actual information written
below is not intended to be factual.
The charge on each drop is found from its v+,vo and v- values, using vo to determine the radius, and thus the mass, of the droplet, and v+ and v- then to deduce the charge. Here, v+, vo and v- are the measured velocities with which the droplet moves in the presence of an upward directed electric field, no field, and a downward directed electric field, respectively.
From
F=Ma which becomes
F=mg field-free
F=mg-Ee/h field up
F=mg+Ee/h field down
For a droplet subjected to a constant force , a terminal velocity is reached , given by
V= 3.6x1019 (F/m) (1+T/To)
where F and m are the force on and mass of the droplet respectively and T the temperature of the moon’s surface. To is the sun’s surface temperature, taken to be 6000 degrees Kelvin. For a freely falling droplet, the radius a of the droplet can then be determined from vo by
………………………………etc.
Results
Give the results, in a
table, graph or image format. Do not require that the reader have access to the
data book to see what your data is.
The data for the measured flight times are shown in table 1, and the resulting velocity sets for each droplet are shown in table 2. The green points in table 2. were taken during the first phase of the moon, and thus should be multiplied by 1.1, whereas those taken during the final quarter are divided by the same factor.
Etc. You should
include a table showing the actual data. NOTE: Be sure you give the units for EVERY
physical quantity in both your report and your data book!
From these values, mean values of the velocities were deduced. Substitution of these values into equations 1-3 above results in values for e. The results are shown in Table 2.
|
Droplet |
v+(cm/s) |
v+(cm/s) |
v-(cm/s) |
e(up)(10
-19 Coul) |
e(down)(10
-19 Coul) |
|
1 |
0.3 |
0.6 |
0.03 |
1.54+/-0.2 |
1.4+/-0.25 |
|
2 |
0.3 |
0.89 |
0.8 |
1.67+/-0.2 |
1.6+/-0.27 |
|
3 |
0.6 |
0.45 |
0.56 |
1.5+/-0.24 |
1.5+/-0.26 |
|
4 |
0.6 |
0.23 |
0.34 |
1.7+/-0.28 |
1.7+/-0.28 |
|
5 |
0.98 |
0.5 |
0.55 |
1.4+/-0.23 |
1.4+/-0.25 |
|
6 |
0.03 |
0.5 |
0.23 |
1.4+/-0.29 |
2.0+/-0.40 |
Table 2. The velocities are given for each droplet in
columns 2-4, and the corresponding charges in columns 5-6.
The
errors shown represent standard deviations of the means deduced from ten measurements
of each velocity for each droplet.
Figure
2. Plot
of charge (in units of 10 –19 Coulomb) versus drop number.
A display of the resulting e values is shown in figure 2. It is clear that for this set of fabricated data, each droplet had only a single electronic charge. Your data will not look like this. The final value of e is obtained from a weighted average of the data in table 2. The result is
e=(1.53 +/- .03) x 10 –19 C.
Error analysis
Explain how you got
the error bar(s) you placed on your value(s).
The error bar cited above comes from the following sources:
Random error: Error due to human reaction times on the timer, reading the scale, etc., are taken into account by the use of standard deviations of the mean of several time measurements.
Systematic errors: Errors on the following parameters entering into equations 1-3 above are estimated to be:
Electric field: 1% on the meter, .05% on the plate separation
Viscosity of air:.001 %
Temperature of the moon: 40 %
Density of the oil: 50%
The final error cited above is the quadratic combination of the random and the propagated systematic errors.
Discussion and Conclusion
Draw a conclusion. If
you wish to be speculative , here is the place to do
it.
The value found is 9.5 % lower than the accepted value of 1.6 x 10 –19 C and lies outside the quoted error bar.
Before addressing the impact of this finding, we first discuss the precision of the present experiment. The largest factors contributing to the cited error are the temperatures of the moon and the density of the oil. Fortunately the temperature of the moon enters only weakly into equation 3, and when the correct equation is used instead, drops out entirely, so this will not be considered further. The rather large error in the density of the oil drop results from the fact that half of the droplets were not oil at all but styrefoam balls introduced into this laboratory some years ago by a pernicious elf. These balls, which have a density quite different from that of oil, have now infiltrated all the oil in the universe, leading to a decrease in motor longevity nationwide as well as questionable results from Millikan oil drop experiments everywhere. Thus one must add to the error bar cited above the qualification “if true at all”.
Nevertheless, we conclude that there either a serious
problem with Millikan’s value, or that the value has
changed since 1911. Because it is more exciting to think that the universe is
not static than that the freshmen at Caltech could possibly have made a
mistake, we prefer the latter interpretation. From this result we deduce that e
is decreasing by about 2% per century.
Linearly extrapolating this rate results in the prediction that the
value of e will go to zero in the year 7000, at which time atoms will fall
apart completely. This time is significantly less than the lifetime predicted
for the sun using current values of the natural constants, although it probably
References
[1] etc.