How accurately can Millikan's oil-drop method measure electric charge, given that droplets undergo Brownian motion?
In the classic Millikan oil-drop experiment, tiny charged droplets are also jostled by random molecular collisions (Brownian motion): how much does this fundamentally limit the precision of measuring the electron's charge this way?
History and references
Settled by Standard statistical/Brownian-motion error analysis.
Kapitza's problem #98 asks students to analyze how Brownian motion limits the accuracy of Millikan's 1909-1913 oil-drop charge measurements. Einstein's 1905 theory of Brownian motion provides the statistical framework (mean-square displacement growing linearly with time, set by the fluctuation-dissipation relation) needed to quantify the random-walk noise floor on a droplet's measured terminal velocity, and this remains a standard worked example in statistical-physics and experimental-methods courses illustrating how thermal noise fundamentally limits precision measurement.
The same random molecular jostling that Einstein used to prove atoms exist shows up again as the noise floor limiting one of the most famous atomic-scale measurements in physics.
Explanations that circulated
- Millikan's measurement precision is limited only by how well you can time the droplet's fall (Brownian-motion-induced random fluctuations in the droplet's terminal velocity set an additional, fundamental statistical floor on precision, independent of timing skill, that must be averaged down over many measurements)
References
- Statistical fluctuation limits in oil-drop charge measurements (standard treatment building on Einstein's 1905 Brownian motion theory), Standard treatment following Einstein (1905) and Millikan (1913), Textbook / historical physics literature, 2020
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