Answer the following. (a) Calculate the angular momentum of the Moon due to its

Question

Answer the following. (a) Calculate the angular momentum of the Moon due to its orbital motion about Earth. In your calculation use 3.84 108 m as the average Earth-Moon distance and 2.36 106 s as the period of the Moon in its orbit. (Use 7.36 1022 kg for the mass of the moon.) kg · m2/s (b) If the angular momentum of the moon obeys Bohr's quantization rule (L = nPlanck constant) determine the value of the quantum number, n. (c) By what fraction would the Earth-Moon radius have to be increased to increase the quantum number by 1?

Explanation / Answer

a) L = I w = m r^2 2 pi/T = 7.36E22*3.84E8^2*2*pi/2.36E6=2.89E34

b) n = L/hbar = 2.89E34*2*pi/6.63E-34=2.74E68

c) then

dL = hbar

7.36E22*(3.84E8+r)^2*2*pi/2.36E6-7.36E22*3.84E8^2*2*pi/2.36E6=6.63E-34

r = 3.06E-8 m

so fraction = 3.06E-8/3.84E8=7.97E-17

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