 Teaching Physics with the Physics Suite Edward F. Redish

The spinning electron

An electron at rest has an angular momentum equal to h/4p, where h = Planck's constant (6.63 x 10-34 J-s). At one time it was suggested that the electron was a uniform sphere with radius equal to about 2 x 10-15 m. (This value is obtained by setting the electrostatic potential energy of a uniform sphere of charge equal to mc2. You'll carry out this calculation later in the course.) Suppose this were so, and the angular momentum arose from the sphere's rotating with an angular velocity w.

1. Find the value of w required to get the necessary angular momentum.
2. Calculate the speed with which the electron's equator would be rotating.

(Your answer should come out greater than the speed of light. Rumor has it that in the 1920's one student was discouraged from publishing his idea that the electron had a spin by Wolfgang Pauli presenting him with this calculation. The result -- and Pauli's objection -- is wrong for two reasons. First, if the electron were a sphere spinning that fast, one would have to take relativity into account. The classical formula for angular momentum wouldn't hold. Second, as far as we know, the electron isn't a sphere but is about as close as we can get to a true point. It has built in angular momentum anyhow -- but not from spinning!)

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