# Consider the earthsun system as a gravitational analog to the hydrogen atom.(a) What is the potential energy function (replacing Equation 4.52)? (Let m E be the mass of the earth, and M the mass of the sun.)(b) What is the Bohr radius, g , for this system? Work out the actual number.(c) Write down the gravitational Bohr formula, and,

Consider the earth–sun system as a gravitational analog to the hydrogen atom.

(a) What is the potential energy function (replacing Equation 4.52)? (Let m_{E} be the mass of the earth, and M the mass of the sun.)

(b) What is the “Bohr radius,” α_{g}, for this system? Work out the actual number.

(c) Write down the gravitational “Bohr formula,” and, by equating E_{n} to the classical energy of a planet in a circular orbit of radius r_{0}, show that From this, estimate the quantum number n of the earth.

(d) Suppose the earth made a transition to the next lower level (n-1). How much energy (in Joules) would be released? What would the wavelength of the emitted photon (or, more likely, graviton) be? (Express your answer in light years—is the remarkable a coincidence?)

Equation 4.52

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**Related Book For**

## Introduction To Quantum Mechanics

3rd Edition

Authors: David J. Griffiths, Darrell F. Schroeter

ISBN: 9781107189638