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 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 coulombs (SI unit for electric charge).

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.

Contents 1 Experimental procedure 1.1 The apparatus 1.2 Method 2 Millikan's experiment and cargo cult science 3 External links and references 4 More external links

[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 (actually they look more like dots). 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 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

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,^[1] 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,^[2] 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] External links and references

1. ^ NIST Reference on Constants, Units and Uncertainty
2. ^ "The electron and the light-quant from the experimental point of view" by Millikan, Robert A. held in Stockholm (May 23, 1924). Retrieved on 2006-11-12

• Karlsson, Magnus, "Millikan's oildrop experiment". (Simplified version)
  • Graphical simulation of the experiment - examples of the difficulties
• 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.

[edit] More external links

• 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
• Cargo cult science, text of the Feynman lecture.
• Millikan Oil Drop Experiment in space. A variation of this experiment has been suggested for the International Space Station.