Oil-drop experiment

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The purpose of Robert Millikan's oil-drop experiment (1909) was to measure the electric charge of the electron. He did this by carefully balancing the gravitational and electric forces on tiny charged droplets of oil suspended between two metal electrodes. Knowing the electric field, the charge on the oil droplet could be determined. Repeating the experiment for many droplets, he found that the values measured were always multiples of the same number. He interpreted this as the charge on a single electron: 1.602 × 10⁻¹⁹ coulomb (SI unit for electric charge).

Contents 1 Background 2 Experimental procedure 2.1 The apparatus 2.2 Method 3 Millikan's experiment and cargo cult science 4 Notes 5 Further reading 6 External links

[edit] Background

Starting in 1909, while a professor at the University of Chicago, Millikan worked on his oil-drop experiment (since repeated, with varying degrees of success, by generations of physics students) in which he measured the charge on a single electron. After a publication on his first results ^[1] in 1910, contradictory observations by Felix Ehrenhaft ^[2] started a controversy between the two physicists. After improving his setup he published his seminal study in 1913. ^[3]

The so-called elementary charge is one of the fundamental physical constants and accurate knowledge of its value is of great importance. His experiment measured the force on tiny charged droplets of oil suspended against gravity between two metal electrodes. Knowing the electric field, the charge on the droplet could be determined. Repeating the experiment for many droplets, Millikan showed that the results could be explained as integer multiples of a common value (1.592 × 10⁻¹⁹ coulomb), the charge on a single electron.

Although at the time of Millikan's oil drop experiments it was becoming clear that there exist such things as subatomic particles, not everyone was convinced. Experimenting with cathode rays in 1897, J.J. Thompson had discovered negatively charged "corpuscles", as he called them, with a mass about 1000 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 beauty of the oil drop experiment is that as well as allowing quite accurate determination of the fundamental unit of charge Millikan's apparatus also provides a "hands on" demonstration that charge is actually quantized. It demonstrates this simply and elegantly. Thomas Edison, who had previously thought that charge is a continuous variable, became convinced after having a go with Millikan's apparatus.

There is some controversy over the use of selectivity in Millikan's results of his second experiment measuring the electron charge. This work was done by Allan Franklin, a former high energy experimentalist and current philosopher of science at the University of Colorado. Franklin contends that, while Millikan's exclusions of data do not affect the final value of e that he obtained, there was substantial "cosmetic surgery" that Millikan performed which had the effect of reducing the statistical error on e. This enabled Millikan to quote the figure that he had calculated e to better than one half of one percent; in fact, if Millikan had included all of the data he threw 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, which Millikan likely tried to avoid.

In 1923, Millikan won the Nobel Prize for physics in part because of this experiment. This experiment has since been repeated by generations of physics students, although it is rather expensive and difficult to do properly.

[edit] Experimental procedure

[edit] The apparatus

The diagram shows a simplified version of Millikan's set up. A uniform electric field is provided by a pair of horizontal, parallel plates with a high potential difference between them. Drops of oil are allowed to drift between them. By varying the voltage, the drops can be made to rise or fall. The plates are held together by a ring of insulating material, with four holes cut into it. A bright light source shines through three of the holes, focussed on the region where the oil drops levitate between the plates. A low-powered microscope is inserted through the other hole. The oil drops reflect the light and look like bright points on a dark field of view through the microscope. The microscope has a graduated scale in the eyepiece which allows the velocity of a drop to be measured by timing how long it takes to travel from one division to another.

The oil is a type that is usually used in vacuum apparatus. This is because this type of oil has an extremely low vapour pressure. Ordinary oil would evaporate away under the heat of the light source, so the mass of the oil drop would not remain constant over the course of the experiment. Some oil drops will pick up a charge through friction with the nozzle as they are sprayed, but more can be charged by including an ionising radiation source (such as an x ray tube).

[edit] 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 W). 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:

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 V 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:

Now at terminal velocity the oil drop is not accelerating. So the total force acting on it must be zero. So the two forces F and W must cancel one another out.
F = W implies:

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

Now the field is turned back on.

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

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. But in practice this is extremely difficult to do precisely. A more practical approach is to turn V up slightly so that the oil drop rises with a new terminal velocity v₂. Then

[edit] Millikan's experiment and cargo cult science

Richard Feynman said in a commencement lecture he gave at Caltech in 1974^[4]

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. We've learned those tricks nowadays, and now we don't have that kind of a disease.

As of 2006, the accepted value for the elementary charge is 1.60217653(14) x 10⁻¹⁹ coulombs,^[5] where the 14 indicates the uncertainty of the last two decimal places. In his Nobel lecture, Millikan gave his measurement as 4.774(5) x 10⁻¹⁰ statcoulombs,^[6] which equals 1.5924(17) x 10⁻¹⁹ coulombs. 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.

[edit] Notes

1. ^ R.A. Millikan, A new modification of the cloud method of determining the elementary electrical charge and the most probable value of that charge, Phys. Mag. XIX, 6(1910), p. 209
2. ^ Ehrenhaft F., Über die Kleinsten Messbaren Elektrizitätsmengen, Phys. Zeit., 10(1910), p. 308
3. ^ R.A. Millikan, On the Elementary Electric charge and the Avagadro Constant, Phys. Rev. II, 2(1913), p. 109
4. ^ Richard Feynman. Cargo Cult Science.
5. ^ NIST Reference on Constants, Units and Uncertainty
6. ^ Millikan, Robert A.. "The electron and the light-quant from the experimental point of view" Stockholm (May 23, 1924). Retrieved on 2006-11-12

[edit] Further reading

• Seyway, 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. 

[edit] External links

• Karlsson, Magnus, "Millikan's oildrop experiment". Simplified Java applet simulation of the experiment.
• 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.
• Delpierre, G.R. and B.T. Sewell, "Millikan's Oil Drop Experiment". 25 April 2005
• Engeness, T.E., "The Millikan Oil Drop Experiment". 25 April 2005
• Millikan R. A. (1913). "On the elementary electrical charge and the Avogadro constant". The Physical Review, Series II 2: 109–143. , Paper by Millikan discussing modifications to his original experiment to improve its accuracy.
• Millikan Oil Drop Experiment in space. A variation of this experiment has been suggested for the International Space Station.