Problem 6. (30 points) The correspondence principle. In this problem we will explore the correspondence principle. (a) What does the correspondence principle say? (b) Suppose we consider the Earth's orbit around the Sun as an analogue of the electron's orbit around the nucleus of the Hydrogen atom. Calculate the magnitude of the angular momentum L of the Earth. (Use that M.=5.97 . 104 kg and R Earth =1.50 . 10m m.) (c) We will pretend to quantize the Earth's orbit the same way we did with Bohr's model of the hydrogen atom. This means that we assume that the magnitude of the angular momentum of the Earth is quantized in units of h as L = nh. Use your result in (b) to determine the Earth's quantum number n from this quantization condition. (Yes, it is going to be a very big number!) (d) Mimic the calculations from the hydrogen atom to calculate the energy levels E, in the Earth-Sun system (now replacing the Coulomb force law with Newton's law). (e) How much energy is released if the Earth transitions from its current state n (with the value of n from part c) to the next state with n -1? (Hint: you are going to need a Taylor expansion you worked out in HWO.) (f) What is the change in the radius under such a transition? (g) Interpret your results from the Earth-Sun "atom" using the correspondence principle