Many subatomic particles (including the electron) behave as if they were spinnin

Question

Many subatomic particles (including the electron) behave as if they were spinning around their axis. Measurements indicate that the electron has a spin angular momentum of h/4pi, where h is Planck's constant. A simplistic model imagines the electron to be a spinning spherical ball of uniform density. Other measurements indicate that if the electron really is a spherical ball, its radius must be less than 10^-18 m.

Show that if the simplistic model were true, the speed of the surface of the electron would be much faster than the speed of light.

(A more sophisticated quantum-mechanical model of electron spin avoids this paradox.)

Explanation / Answer

L =h/4pi

mass of electron m =9.1x10^-31 kg, r=10^-18m

h =6.63x10-34Js

Angular momentum L =mvr

v =L/mr = h/4pi x mr

v =6.63x10-34/ (4x3.14x9.1x10-31x10-18 )

v =5.8x1013 m/s

Velcoity of light is 3x108 m/s

So velocity of given electron is greater than speed of light.

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