If the angular momentum of Earth in its motion around the Sun werequantized like

Question

If the angular momentum of Earth in its motion around the Sun werequantized like a hydrogen electron according to Equation 4-17(Bohr's quantization of the angular momentum L); L = mvr = nh/2pi = nh(with a cross), what would Earth's quantum number be? How much energy would bereleased in a transition to the next lowest level? Would thatenergy release (presumably as a gravity wave) be detectable? Whatwould be the radius of that orbit? (The radius of Earth's orbit is1.50x10^11 m.) L = mvr = nh/2pi = nh(with a cross), what would Earth's quantum number be? How much energy would bereleased in a transition to the next lowest level? Would thatenergy release (presumably as a gravity wave) be detectable? Whatwould be the radius of that orbit? (The radius of Earth's orbit is1.50x10^11 m.)

Explanation / Answer

I am having trouble figuring out the change in the radius of theorbit (part three of the question). The answer suggests using R((n+1)/ n). Is R the radius of the Earth? And how do you derivethis equation?

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