# Orbit about star, emission spectrum of light

1. Jun 9, 2013

### unscientific

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. Jun 10, 2013

### unscientific

anyone?

3. Jun 10, 2013

### milesyoung

Have you found an expression for the frequency of revolution of the proton around the black hole?

4. Jun 10, 2013

### unscientific

Yes, it is simply the above * 10-6. Problem is, to solve for M and r, I need at least 1 more equation