In the Classroom edited by
JCE DigiDemos: Tested Demonstrations
Ed Vitz Kutztown University Kutztown, PA 19530
Magnet and BB Analogy for Millikan’s Oil-Drop Experiment submitted by:
Earl F. Pearson Department of Chemistry, Middle Tennessee State University, Murfreesboro, TN 37132;
[email protected] checked by:
M. Dale Alexander Department of Chemistry and Biochemistry, New Mexico State University, Las Cruces, NM 88003-8001
In a previous article in this Journal (1), Millikan’s original data (2) were analyzed using Microsoft Excel. As expected, Millikan’s results from 1911 were almost identical to that obtained by computer using a modern spreadsheet program. This article describes the results of a typical classroom demonstration that I have performed many times in my first-semester freshman chemistry class for chemistry and pre-professional majors.1 With a few slight modifications, this demonstration could also become a hands-on laboratory experiment. As an introduction to the exercise, ask the students if they can think of a way to determine the mass of a single BB without weighing any known number of BBs. Then tell the class that prior to 1911, Millikan developed a way to measure the charge of a single electron without ever measuring the charge of any known number of electrons. Remind the class that Millikan received the Nobel Prize in Physics for this work. This usually gets the class thinking and receptive to the underlying scientific logic of Millikan’s oil drop experiment that is illustrated in the demonstration that follows. Experimental The “oil” drops are cut from strips of “refrigerator magnets” used in arts and crafts. These strips are only about 0.5 inches wide and this limits the size of the resulting oil drops. The magnetic material is cut into teardrop shapes to simulate the oil drops. Usually about 20 drops of varying sizes are sufficient. The BBs were Copperhead brand. (The BBs are not copper as they appear; they are copper-coated steel and are attracted to a magnet.) All these materials were purchased at Wal-Mart. The magnetic oil drops are dropped into a Petri dish containing the BBs (electrons). Once the BBs are attached to the magnetic drops, each drop is removed from the dish of BBs. (The backing tape can be removed from the drops to allow BBs to stick to both sides.) The BBs are dislodged from the oil drops onto a weighing dish that was previously tared to zero mass on a Mettler PC 4400 balance.2 Refrigerator magnets and magnetic cards have low magnetic fields and do not attract a large number of BBs. However, in performing the experiment many times, I have always found them to produce a good range for the number of BBs on each drop. This is important for producing a good data set with few identical masses for the BBs on the drops. It might be pos-
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sible to use small ceramic magnets (from Radio Shack or Edmund Scientific) and break them into different size pieces. If the sizes of the pieces are different, these stronger magnets should attract more BBs and would possibly lead to many non-duplicated data sets. However, one should be careful that fragments of the magnet do not cling to the BBs as they are removed for weighing. One should also try any modifications of the demonstration many times to ensure that at least one difference does in fact represent the mass of a single BB every time the demonstration is performed. This has always happened for me using refrigerator magnets. While Millikan did not remove the electrons from the oil drops, he did use a technique that measured only the combined charge of all the electrons on the oil droplets. His measurement of charge was only sensitive to the number of electrons on the oil drops and also sensitive to the mass of the drop, which he separately measured. Since the BBs and the oil drop share the property of mass, removing the BBs and weighing them separately is necessary to measure only the mass of the BBs. However, this operation is analogous to Millikan separately measuring the mass of his oil drops so that he could determine the charge by watching the rate of fall of the drop through air under the influence of gravity when the voltage on the plates was turned on or off. His experiment measured the combined charge of the particles (electrons) adhering to a single oil drop, just as I determined the combined mass of the particles (BBs) adhering to the individual “oil drops.” He separately measured the mass of all the oil in the drop and I separately measured the combined mass of all the BBs. The mass of BBs on each drop is recorded to the precision of the balance used. (A three decimal place balance is a little better but, as illustrated here, a 0.01-g balance can be used.) I usually also prepare one oil drop that is much larger than the others (or use a very small high-strength magnet) and leave these BBs on the weighing dish as a final demonstration of the accuracy of the determination of the mass. Once the mass of a single BB is determined, the number of BBs on the final drop is calculated. Every time I have done this demonstration the calculated number of BBs for the final drop has been correct. A 0.001 g balance will allow a larger number of BBs for the final measurement using the larger drop or high-field magnet with little chance of calculating a wrong number of BBs on the large drop.
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In the Classroom Table 1. Mass of BBs Attached to Magnetic Tape Classroom Demonstration Data
Microsoft Excel Spreadsheet Analysis of Data
Mass Mass Unique Drop of Sorted Mass BBs/g /g /g
∆Mass /g
Calc. No. of BBs
01 01.97 10.78 10.78
---
32.667
33
0.1111
02 02.64 05.61 05.60
5.18
17.000
17
0.0000
03 01.60 05.59 05.27
0.33
16.939
17
0.0037
04 02.00 05.30 04.90
0.37
16.061
16
0.0037
05 02.63 05.24 04.59
0.31
15.879
16
0.0147
06 01.94 04.91 04.25
0.34
14.879
15
0.0147
07 02.59 04.89 03.90
0.35
14.818
15
0.0331
08 02.60 04.89 03.59
0.31
14.818
15
0.0331
09 02.00 04.60 03.27
0.32
13.939
14
0.0037
10 02.95 04.60 02.93
0.34
13.939
14
0.0037
11 02.28 04.57 02.62
0.31
13.848
14
0.0230
12 02.28 04.25 02.29
0.33
12.879
13
0.0147
13 02.91 03.91 01.97
0.32
11.848
12
0.0230
14 01.66 03.90 01.63
0.34
11.818
12
0.0331
15 02.60 03.89 01.31
0.32
11.788
12
0.0450
a
16 02.63 03.62
---
17 02.63 03.59
0.33
Whole 2c No. (∆BB) of BBs
10.970
11
0.0009
10.879
11
0.0147
18 01.31 03.59
10.879
11
0.0147
19 01.94 03.57
10.818
11
0.0331
20 02.92 03.27
09.909
10
0.0083
21 02.30 02.95
08.939
09
0.0037
22 05.59 02.92
08.848
09
0.0230
23 03.27 02.91
08.818
09
0.0331
24 04.60 02.64
08.000
08
0.0000
25 03.59 02.63
07.970
08
0.0009
25 04.60 02.63
07.970
08
0.0009
27 03.91 02.63
07.970
08
0.0009
28 03.90 02.60
07.879
08
0.0147
29 04.89 02.60
07.879
08
0.0147
30 05.24 02.59
07.848
08
0.0230
31 04.91 02.30
06.970
07
0.0009
32 03.62 02.28
06.909
07
0.0083
33 01.98 02.28
06.909
07
0.0083
34 03.59 02.00
06.061
06
0.0037
35 05.61 02.00
06.061
06
0.0037
36 03.57 01.98
06.000
06
0.0000
37 03.89 01.97
05.970
06
0.0009
38 04.57 01.94
05.879
06
0.0147
39 04.89 01.94
05.879
06
0.0147
40 04.25 01.66
05.030
05
0.0009
41 05.30 01.60
04.848
05
0.0230
42 10.78 01.31
03.970
04
0.0009
b
a
Minimal difference between two adjacent masses of the BBs. b c Average mass of the BBs. Square of the difference between the calculated and whole number of the BBs.
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Analysis of Data In the classroom demonstration, after the masses of the BBs on each drop are recorded on the board (column 2 in Table 1), the values are sorted from largest to smallest (column 3). The class helps by calling out the masses in order from the original column of data as the instructor writes them in descending order in a another column on the board. Mark through each mass in the first column as it is recorded in the second column. Some masses may differ by about the precision of the balance used. These masses obviously represent the same number of BBs and should be averaged to obtain another column of unique masses (column 4). Subtracting each value from the one just above it creates another concern. There will be several duplicate differences and some differences that will represent the minimum difference between two adjacent masses (column 5). The smallest difference between pairs of drops should correspond to a single BB. These unique differences are used to determine the average mass of a BB. The average is recorded as the final value in the column of differences (column 5). The number of BBs on each drop (column 6) is determined by dividing the average mass just determined into the total mass of BBs on each drop in the sorted mass column. The actual number of BBs is obtained by rounding each value to the nearest whole number (column 7). The average mass is also used to determine the number of BBs that was attached to the last large drop. It is particularly dramatic to use a very small rare-earth magnet as the last drop. As a finale, the BBs for the largest oil drop are dramatically counted one by one as I drop them into a dish to show that the result for the mass of a single BB was correctly determined. If more time is available, I suggest a variation of the demonstration. Measure the mass of the final large drop without removing the BBs and, after the mass of a single BB is determined, ask the students how to determine both the mass of the large magnet and the number of BBs on it. This would be a good group project followed by class discussion to arrive at a method that should work. The class should come up with the idea that the difference in mass of the two largest drops can be used to determine how many extra BBs the largest drop has over that on the next largest drop. The number of BBs on the largest drop is obtained by adding the number of BBs on the next-to-largest drop to the number of extra BBs on largest drop. The mass of the magnet is determined by subtracting the mass of the BBs on the largest drop from the total mass of the drop. You can still count the number of BBs dramatically to show the method worked and also measure the mass of the largest drop for additional confirmation. Typical data that have been analyzed using Microsoft Excel are shown in Table 1. The data are analyzed in the same fashion as previously described (1) on Millikan’s original data (2). The squared deviations are shown in the last column and the variance about regression is calculated to be 0.15517. The data are plotted from Excel in Figure 1. The best value for the mass of a single BB is the slope of the linear regression line of a plot of the total mass ( y axis) against the whole number of BBs (x axis). It should be noted that the average value, 0.33 g (last entry in column 5) is not significantly different from the regression value, 0.3272.
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In the Classroom
The least-square fit is slightly improved (variance about regression goes from 0.015517 to 0.009151) by using the regression value in calculating the number of BBs on each drop.
Refrigerator magnets and BBs can be used as an effective analogy to explain Millikan’s oil-drop experiment. The demonstration is simple and easy for chemistry students to comprehend. Its close analogy to the original work of Millikan makes it easier for students to understand and remember the important features of Millikan’s classical experiment. The demonstration dispels the notion that somehow the actual charge of a single electron was “factored” from the total charge measured on each drop. See if you can look at the second column of Table 1 and easily identify the common factor of 0.3272! This demonstration could be modified and used as an experiment in high school or first-year college chemistry laboratories. Another modification could use a “standardized” mass for all the oil drops by using identical ceramic magnets. Then the total mass including the magnet could be determined for each drop with the BBs still attached. The difference in mass of pairs of drops would subtract out the mass of the magnet and allow the mass of a single BB to be determined. In order to calculate the number of BBs on any drop, including the last large drop, one would have to measure the mass of the magnet in a separate experiment or use the y-axis intercept from the regression line. When the mass of the last large drop is determined, the BBs could be removed and placed in a separate dish. The mass of the magnet alone could then be measured. The total mass of the BBs on the large drop is the difference between its total mass and the measured mass of the magnet. One could then calculate the number of BBs by dividing the mass of BBs on the last drop by the mass of a single BB. It would also be possible to determine the mass of the magnet by counting the number of BBs on the final large drop and multiplying by the mass of a single BB. The difference between the total mass of the last drop and the calculated mass of all the BBs would represent the mass of the magnet. One could then compare the mass of the magnet determined from the data and the actual mass of the magnet. The mass of a BB could be measured and compared to the mass determined from the data. This might be an interesting alternate approach to the demonstration that could arguably be a closer analogy to Millikan’s experiment since the BBs would not be removed from the drops used in determining the mass of a single BB just as he did not remove the electrons from the drop in determining the charge of the electron. However if all the magnets were of identical mass (and, therefore of identical magnetic field strength), most of them would likely attract the same number of BBs and likely produce many duplicates of the same mass of BBs. In the extreme, one might not have any two masses that represented a difference of exactly one BB. Strong field magnets might have a smallest difference representing 0, 2, 3, 4, ... BBs. If no pair of masses differs by exactly one BB, the analysis of the data will be more difficult, but still possible. It is even www.JCE.DivCHED.org
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10
Total Mass / g
Discussion
12
8
6
4
y = 0.3272x R 2 = 0.9998
2
0 0
10
20
30
40
Number of BBs Figure 1. Excel plot of data from Table 1.
possible that the strong field magnets might be attracted by ferrous parts within the balance and cause undetermined errors. Using “standardized” magnets should be tested carefully before it is tried with a class. Another interesting analogy to Millikan’s oil-drop experiment was published in this Journal by Doris Eckey (3). This article uses the price of candies to illustrate how the price of an individual piece can be determined by factoring the price of the entire bag by the number of pieces to determine the price per piece of candy. This analogy also helps students to understand the underlying principles involved in Millikan’s oil-drop experiment. A Google search using “Millikan oil-drop experiment” resulted in 10,200 entries. Two interesting simulations were found (4, 5). The first link is to a QuickTime animation with an audio explanation. It illustrates the important features of Millikan’s experiment and identifies the charge on each drop as an integral multiple of the smallest charge observed. However, Millikan identified the fundamental charge as the smallest DIFFERENCE in charge between different pairs of drops. It is not necessary that one find a drop with only one electron on it. The second site is a simulation that allows one to focus on a single droplet as was done by Millikan and adjust the voltage so that the drop falls, rises, or remains motionless. This site makes an important point that is often missed in textbook discussions. An individual drop will randomly change its total charge as the droplet picks up or loses charges and abruptly change its velocity and even direction of motion. It is possible to determine the set of voltages that result in an individual drop remaining motionless after each abrupt change in its charge. The latter Web site introduces “random” errors into the values. Another interesting Web site (6) contains links to printable copies of Millikan’s more refined article (7) including his most accurate determination of other fundamental constants, such as Avogadro’s number, that could also be obtained from his data. The site also contains a link to an article by Harvey Fletcher (8), Millikan’s graduate student, who helped determine the fundamental charge of the electron. Fletcher was somewhat disappointed that Millikan did not include him as a coauthor on the original article that led to
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In the Classroom
the Nobel Prize in Physics. It should be noted that Millikan had already made measurements of the fundamental charge before Fletcher joined his research group. Millikan was also instrumental in getting Fletcher admitted to graduate school. These articles are interesting connections to the history of one of the most elegant pieces of experimental science that has ever been produced.
Literature Cited 1. 2. 3. 4.
5.
Notes 1. This demonstration was presented at the 15th BCCE at the University of Waterloo in Waterloo, Canada, August 9–13, 1998. 2. The precision of this balance is ±0.01 g, demonstrating that balance precision is not critical.
6. 7. 8.
Pearson, Earl F. J. Chem. Educ. 2005, 82, 851–854. Millikan, R. A. Phys. Rev. 1911, 32, 349–397. Eckey, D. J. Chem. Educ. 1996, 73, 237–238. Millikan Oil-Drop Experiment. http://chemistry.umeche. maine.edu/~amar/fall2004/Millikan.html (accessed June 2006). Millikan Oil-Drop Experiment. http://www.hesston.edu/academic/FACULTY/NELSONK/PhysicsResearch/Millikan/ millikan.html (accessed June 2006). Robert Andrews Millikan Biography. http://www.aip.org/history/ gap/Millikan/Millikan.html (accessed June 2006). Millikan, R. A. Phys. Rev. Series II 1913, 2, 109–143. Fletcher, Harvey. Physics Today 1982, June, 43–47.
This article has been developed into a JCE Classroom Activity: “Millikan: Good to the Last (Oil) Drop” by Earl F. Pearson See pages 1312A–B in this issue.
JCE Classroom Activities
Find all 82 Activities at JCE Online
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