The Millikan Oil-Drop Experiment The charge of an electron was first measured by the American physicist Robert Millikan during 1909-1913.


The Millikan Oil-Drop Experiment The charge of an electron was first measured by the American physicist Robert Millikan during 1909-1913. In his experiment, oil is sprayed in very fine drops (around 10-4 mm in diameter) into the space between two parallel horizontal plates separated by a distance d. A potential difference V AB is maintained between the parallel plates, causing a downward electric field between them. Some of the oil drops acquire a negative charge because of frictional effects or because of ionization of the surrounding air by x rays or radioactivity. The drops are observed through a microscope.
(a) Show that an oil drop of radius r at rest between the plates will remain at rest if the magnitude of its charge is q = 4π/3 pr3gd/ V AB
Where p is the density of the oil (ignore the buoyant force of the air.) By adjusting V AB to keep a given drop at rest, the charge on that drop can be determined, provided its radius is known.
(b) Millikan€™s oil drops were much too small to measure their radii directly.
Instead, Millikan determined r by cutting off the electric field and measuring the terminal speed v, of the drop as it fell. (We discussed the concept of terminal speed in Section 5.3.) The viscous force F on a sphere of radius r moving with speed u through a fluid with viscosity η is given by Stokes's law: F = 6πηru. When the drop is falling at uv the viscous force just balances the weight w = mg of the drop. Show that the magnitude of the charge on the drop is

9 = 187 2p8 VAB V 2pg
Within the limits of their experimental error, every one of the thousands of drops that Millikan and his coworkers measured had a charge equal to some small integer multiple of a basic charge e. That is, they found drops with charges of ±2e, ±5e, and so on, but none with values such as 0.76e or 2.4ge. A drop with charge €“e bas acquired one extra electron; if its charge is - 2e, it bas acquired two extra electrons, and so on.
(c) A charged oil drop in a Millikan oil-drop apparatus is observed to fall 1.00 mm at constant speed in 39.3 s if VAB = 0. The same drop can be held at rest between two plates separated by 1.00 mm if VAB = 9.16 V. How many excess electrons bas the drop acquired, and what is the radius of the drop? The viscosity of air is 1.81 X 10-5 N€¢ s/m2 and the density of the oil is 824 kg/m3

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College Physics

ISBN: 978-0495113690

7th Edition

Authors: Raymond A. Serway, Jerry S. Faughn, Chris Vuille, Charles A. Bennett

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Question Posted: March 26, 2010 05:45:10