Oil drop experiment

Millikan's setup for the oil drop experiment

The oil drop experiment was performed by Robert A. Millikan and Harvey Fletcher in 1909 to measure the elementary electric charge (the charge of the electron).

The experiment entailed observing tiny charged droplets of oil between two horizontal metal electrodes. First, with zero applied electric field, the terminal velocity of a droplet was measured. At terminal velocity, the drag force equals the gravitational force, and these depend on the radius in different ways, so that the radius of the droplet, and therefore the mass and gravitational force, could be determined (using the known density of the oil). Then an adjustable voltage was applied between the plates to induce an electric field, and the voltage was adjusted until the drops were suspended in mechanical equilibrium, indicating that the electrical force and the gravitational force were balanced. Now using the known electric field, Millikan and Fletcher could determine the charge on the oil droplet. By repeating the experiment for many droplets, they confirmed that the charges were all small integer multiples of a certain base value, which was found to be 1.5924(17)×10⁻¹⁹ C, less than a 1% difference from the currently accepted value of 1.602176487(40)×10⁻¹⁹ C.^[1] They proposed that this was the (negative of the) charge of a single electron.

Background

Robert A. Millikan in 1891

Starting in 1908, while a professor at the University of Chicago, Millikan, with the significant input of Fletcher,^[2] and after improving his setup, published his seminal study in 1913.^[3] This remains controversial since papers found after Fletcher's death describe events in which Millikan coerced Fletcher into relinquishing authorship as a condition for receiving his PhD.^[4][5] In return, Millikan used his influence in support of Fletcher's career at Bell Labs.

Millikan and Fletcher's experiment involved measuring the force on oil droplets in a glass chamber sandwiched between two electrodes, one above and one below. With the electrical field calculated, he could measure the droplet's charge, the charge on a single electron being (1.592×10⁻¹⁹ C). At the time of Millikan and Fletcher's oil drop experiments, the existence of subatomic particles was not universally accepted. Experimenting with cathode rays in 1897, J. J. Thomson had discovered negatively charged "corpuscles", as he called them, with a mass about 1840 times smaller than that of a hydrogen atom. Similar results had been found by George FitzGerald and Walter Kaufmann. Most of what was then known about electricity and magnetism, however, could be explained on the basis that charge is a continuous variable; in much the same way that many of the properties of light can be explained by treating it as a continuous wave rather than as a stream of photons.

The elementary charge e is one of the fundamental physical constants and its accurate value is of great importance. In 1923, Millikan won the Nobel Prize in physics, in part because of this experiment.

Aside from the measurement, the beauty of the oil drop experiment is that it is a simple, elegant hands-on demonstration that charge is actually quantized. Thomas Edison, who had previously thought of charge as a continuous variable, became convinced after working with Millikan and Fletcher's apparatus.^[6] This experiment has since been repeated by generations of physics students, although it is rather expensive and difficult to conduct properly.

In the last two decades, several computer-automated experiments have been conducted to search for isolated fractionally charged particles. So far (2015), no evidence for fractional charge particles was found after measuring over 100 million drops.^[7]

Experimental procedure

Apparatus

Simplified scheme of Millikan’s oil drop experiment

Oil drop experiment apparatus

Millikan’s and Fletcher's apparatus incorporated a parallel pair of horizontal metal plates. By applying a potential difference across the plates, a uniform electric field was created in the space between them. A ring of insulating material was used to hold the plates apart. Four holes were cut into the ring, three for illumination by a bright light, and another to allow viewing through a microscope.

A fine mist of oil droplets was sprayed into a chamber above the plates. The oil was of a type usually used in vacuum apparatus and was chosen because it had an extremely low vapour pressure. Ordinary oil would evaporate under the heat of the light source causing the mass of the oil drop to change over the course of the experiment. Some oil drops became electrically charged through friction with the nozzle as they were sprayed. Alternatively, charging could be brought about by including an ionising radiation source (such as an X-ray tube). The droplets entered the space between the plates and, because they were charged, could be made to rise and fall by changing the voltage across the plates.

Method

Initially the oil drops are allowed to fall between the plates with the electric field turned off. They very quickly reach a terminal velocity because of friction with the air in the chamber. The field is then turned on and, if it is large enough, some of the drops (the charged ones) will start to rise. (This is because the upwards electric force F_E is greater for them than the downwards gravitational force F_g, in the same way bits of paper can be picked by a charged rubber rod). A likely looking drop is selected and kept in the middle of the field of view by alternately switching off the voltage until all the other drops have fallen. The experiment is then continued with this one drop.

The drop is allowed to fall and its terminal velocity v₁ in the absence of an electric field is calculated. The drag force acting on the drop can then be worked out using Stokes' law:

$F_{d} = 6\pi r \eta v_1 \,$

where v₁ is the terminal velocity (i.e. velocity in the absence of an electric field) of the falling drop, η is the viscosity of the air, and r is the radius of the drop.

The weight w is the volume D multiplied by the density ρ and the acceleration due to gravity g. However, what is needed is the apparent weight. The apparent weight in air is the true weight minus the upthrust (which equals the weight of air displaced by the oil drop). For a perfectly spherical droplet the apparent weight can be written as:

$\boldsymbol{w}=\frac{4\pi}{3}r^3(\rho-\rho_{air})\boldsymbol{g}$

At terminal velocity the oil drop is not accelerating. Therefore, the total force acting on it must be zero and the two forces F and w must cancel one another out (that is, F = w). This implies

$r^2 = \frac{9 \eta v_1}{2 g (\rho - \rho _{air})}. \,$

Once r is calculated, w can easily be worked out.

Now the field is turned back on, and the electric force on the drop is

$F_E = q E \,$

where q is the charge on the oil drop and E is the electric field between the plates. For parallel plates

$E = \frac{V}{d} \,$

where V is the potential difference and d is the distance between the plates.

One conceivable way to work out q would be to adjust V until the oil drop remained steady. Then we could equate F_E with w. Also, determining F_E proves difficult because the mass of the oil drop is difficult to determine without reverting to the use of Stokes' Law. A more practical approach is to turn V up slightly so that the oil drop rises with a new terminal velocity v₂. Then

$q\boldsymbol{E}-\boldsymbol{w}=6\pi\eta\boldsymbol{(r\cdot v _2)}=\left|\boldsymbol{\frac{v_2}{v_1}}\right|\boldsymbol{w}$.

Fraud allegations

There is some controversy raised by the historian Gerald Holton over the use of selectivity in the results of Millikan's second experiment measuring the electron charge. Holton (1978) pointed out that Millikan disregarded the data from a large set of the oil drops in his experiments without apparent reason. Allan Franklin, a former high energy experimentalist and philosopher of science at the University of Colorado has tried to rebut this point by Holton.^[8] Franklin contends that Millikan's exclusions of data did not affect his final value of e but concedes that there was substantial "cosmetic surgery" that Millikan performed which had the effect of reducing the statistical error on e. This enabled Millikan to claim that he had calculated e to better than one half of one percent; in fact, if Millikan had included all of the data he had thrown out, it would have been to within 2%. While this would still have resulted in Millikan having measured e better than anyone else at the time, the slightly larger uncertainty might have allowed more disagreement with his results within the physics community. David Goodstein counters that Millikan plainly states that he had included only drops that had undergone a "complete series of observations" and excluded no drops from this group.^[9]

Millikan's experiment as an example of psychological effects in scientific methodology

In a commencement address given at the California Institute of Technology (Caltech) in 1974 (and reprinted in Surely You're Joking, Mr. Feynman! in 1985 as well as in The Pleasure of Finding Things Out in 1999), physicist Richard Feynman noted:

We have learned a lot from experience about how to handle some of the ways we fool ourselves. One example: Millikan measured the charge on an electron by an experiment with falling oil drops, and got an answer which we now know not to be quite right. It's a little bit off because he had the incorrect value for the viscosity of air. It's interesting to look at the history of measurements of the charge of an electron, after Millikan. If you plot them as a function of time, you find that one is a little bit bigger than Millikan's, and the next one's a little bit bigger than that, and the next one's a little bit bigger than that, until finally they settle down to a number which is higher.

Why didn't they discover the new number was higher right away? It's a thing that scientists are ashamed of—this history—because it's apparent that people did things like this: When they got a number that was too high above Millikan's, they thought something must be wrong—and they would look for and find a reason why something might be wrong. When they got a number close to Millikan's value they didn't look so hard. And so they eliminated the numbers that were too far off, and did other things like that...^[10][11]

As of 2014, the accepted value for the elementary charge is 1.602176565(35)×10⁻¹⁹ C,^[12] where the (35) indicates the uncertainty of the last two decimal places. In his Nobel lecture, Millikan gave his measurement as 4.774(5)×10⁻¹⁰ statC,^[13] which equals 1.5924(17)×10⁻¹⁹ C. The difference is less than one percent, but it is more than five times greater than Millikan's standard error, so the disagreement is significant.

Notes and references

1. "Robert Millikan". APS Physics. Retrieved 26 April 2016.
2. Niaz, Mansoor (2000). "The Oil Drop Experiment: A Rational Reconstruction of the Millikan–Ehrenhaft Controversy and Its Implications for Chemistry Textbook" (PDF). Journal of Research in Science Teaching 37 (5): 480–508. doi:10.1002/(SICI)1098-2736(200005)37:5<480::AID-TEA6>3.0.CO;2-X.
3. Millikan, R. A. (1913). "On the Elementary Electric charge and the Avogadro Constant". Phys. Rev. 2 (2): 109–143. Bibcode:1913PhRv....2..109M. doi:10.1103/PhysRev.2.109.
4. Perry, Michael F. (May 2007). "Remembering The Oil Drop Experiment". Physics Today 60 (5): 56. doi:10.1063/1.2743125.
5. Fletcher, Harvey (June 1982). "My Work with Millikan on the Oil-drop Experiment". Physics Today 43. doi:10.1063/1.2915126.
6. Bandrawal, Praveen Kumar (11 March 2009). Nobel Awards Winner Physics. Pinnacle Technology. pp. 169–. ISBN 978-1-61820-254-3. Retrieved 14 December 2012.
7. "SLAC – Fractional Charge Search – Results". Stanford Linear Accelerator Center. January 2007. Retrieved 8 April 2015.
8. Franklin, A. (1997). "Millikan's Oil-Drop Experiments". The Chemical Educator 2 (1): 1–14. doi:10.1007/s00897970102a.
9. Goodstein, D. (2000). "In defense of Robert Andrews Millikan". Engineering and Science (Pasadena, California: Caltech Office of Public Relations) 63 (4): 30–38.
10. Feynman, Richard, "Cargo Cult Science" (adapted from 1974 California Institute of Technology commencement address), Donald Simanek's Pages, Lock Haven University, rev. August 2008.
11. Feynman, Richard Phillips; Leighton, Ralph; Hutchings, Edward (1997-04-01). "Surely you're joking, Mr. Feynman!": adventures of a curious character. New York: W. W. Norton & Company. p. 342. ISBN 978-0-393-31604-9. Retrieved 10 July 2010.
12. "elementary charge e". NIST Reference on Constants, Units and Uncertainty. National Institute of Standards and Technology. Retrieved 8 April 2015.
13. Millikan, Robert A. (May 23, 1924). The electron and the light-quant from the experimental point of view (Speech). Stockholm. Retrieved 2006-11-12.

Further reading

• Serway, Raymond A.; Faughn, Jerry S. (2006). Holt: Physics. Holt, Rinehart and Winston. ISBN 0-03-073548-3.
• Thornton, Stephen T.; Rex, Andrew (2006). Modern Physics for Scientists and Engineers (3rd ed.). Brooks/Cole. ISBN 0-495-12514-8.
• Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks/Cole. ISBN 0-534-40842-7.

External links

• Simulation of the oil drop experiment (requires JavaScript)
• Thomsen, Marshall, "Good to the Last Drop". Millikan Stories as "Canned" Pedagogy. Eastern Michigan University.
• CSR/TSGC Team, "Quark search experiment". The University of Texas at Austin.
• The oil drop experiment appears in a list of Science's 10 Most Beautiful Experiments originally published in the New York Times.
• Engeness, T.E., "The Millikan Oil Drop Experiment". 25 April 2005.
• Millikan R. A. (1913). "On the elementary electrical charge and the Avogadro constant" (PDF). Physical Review. Series II 2: 109–143. Bibcode:1913PhRv....2..109M. doi:10.1103/PhysRev.2.109., Paper by Millikan discussing modifications to his original experiment to improve its accuracy.
• Hudspeth, P. and Klingler, R., A search for free quarks in the micro gravity environment of the International Space Station , AIP Conf. Proc. 504, 715 (2000). A variation of this experiment has been suggested for the International Space Station.
• Perry, M. F., "Remembering the oil-drop experiment", Physics Today, May 2007, 56-60.