Problem 4.17 Consider the earth-sun system as a gravitational analog to the hydro- gen atom. (a) What is the potential energy function (replacing Equation 4.52)? (Let m be the mass of the earth, and M the mass of the sun.) (b) What is the "Bohr radius," ag, for this system? Work out the actual number. (c) Write down the gravitational "Bohr formula," and, by equating En to the classical energy of a planet in a circular orbit of radius ro, show that n = √ro/ag. 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

Problem 4.17 Consider the earth-sun system as a gravitational analog to the hydro- gen atom. (a) What is the potential energy function (replacing Equation 4.52)? (Let m be the mass of the earth, and M the mass of the sun.) (b) What is the "Bohr radius," ag, for this system? Work out the actual number. (c) Write down the gravitational "Bohr formula," and, by equating En to the classical energy of a planet in a circular orbit of radius ro, show that n = √ro/ag. 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

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

Problem 4.17 Consider the earth-sun system as a gravitational analog to the hydro-
gen atom.
(a) What is the potential energy function (replacing Equation 4.52)? (Let m be
the mass of the earth, and M the mass of the sun.)
(b) What is the "Bohr radius," ag, for this system? Work out the actual number.
(c) Write down the gravitational "Bohr formula," and, by equating En to the
classical energy of a planet in a circular orbit of radius ro, show that n =
√ro/ag. 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 answer20 a coincidence?)

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