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Homework Help: Orbit about star, emission spectrum of light

  1. Jun 9, 2013 #1
    1. The problem statement, all variables and given/known data

    Show that in the Bohr model, the frequency of revolution of an electron in its nth

    In classical physics, the frequency of revolution of the electron is equal to the
    frequency of radiation it emits. Show that when n is very large, the frequency of
    revolution is equal to the frequency radiated upon transition of the electron from orbit
    (n+ 1) to n (Bohr’s correspondence principle). [5]
    Assume that a proton is orbiting a black hole under the sole influence of gravity.
    It produces an emission spectrum equivalent to that of a hydrogen atom, but with
    frequencies multiplied by a factor of 10−6
    . Disregarding relativistic effects, calculate
    the mass of the black hole which would explain the observed emission spectrum. Show
    that the radius of the proton’s orbit is proportional to the square of the quantum number
    n and find the radius of the first orbit.


    2. Relevant equations

    3. The attempt at a solution

    1 equation, 2 unknowns. Not sure how to calculate mass of star in the first place..

  2. jcsd
  3. Jun 10, 2013 #2
  4. Jun 10, 2013 #3
    Have you found an expression for the frequency of revolution of the proton around the black hole?
  5. Jun 10, 2013 #4
    Yes, it is simply the above * 10-6. Problem is, to solve for M and r, I need at least 1 more equation
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