Part A. If you treat an electron as a classical spherical object with radius 1.8

Question

Part A. If you treat an electron as a classical spherical object with radius 1.80×1017 m , what angular speed is necessary to produce a spin angular momentum of magnitude 3/4? Use h = 6.63×1034 Js for Planck's constant, recalling that =h/2, and 9.11×1031 kg for the mass of an electron. Express your answer in radians per second to three significant figures.

Part B.

Use the equation v=r relating velocity to radius and angular velocity together with the result of Part A to calculate the speed v of a point at the electron's equator.

Express your answer in meters per second to three significant figures.

Explanation / Answer

Moments of inertia of solid sphere with radius r:

I = (2/5)mr² = (2/5 * 9.11 * 10^-31)(1.80 * 10^-17)^2 = 1.18 * 10^-64 kg/m^2

L = I = (2/5)mr² = sqrt(3/4)

= sqrt(3/4) / (2/5)mr² = (0.866 * 1.05 * 10^-34)/ 1.18 * 10^-64 = 7.706 * 10^29 rad/s

v = r = 7.706 * 10^29 * 1.8 * 10^-17 = 1.387 * 10^13 m/s

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