An electron at rest has an angular momentum equal to h/4pi, where h = Planck\'s

Question

An electron at rest has an angular momentum equal to h/4pi, 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. Suppose this were so, and the angular momentum arose from the sphere's rotating with an angular velocity w.

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

(answer should come out greater than the speed of light)

Explanation / Answer

L = I w w= L/I= (h/4pi)/I I = 2 mr^2 /5= 2 * 9.1 * 10 ^ -31 * 4 * 10 ^ -30 /5 =1.456 * 10 ^-60 hence w= 3.6239 * 10 ^25 v=wr =3.6239 * 10 ^25 * 2 * 10 ^-15=7.258 * 10 ^10 m/s

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