How do you calculate energy levels and transition frequencies in Bohr's model?

[peripatein]

Homework Statement

In Bohr's model the allowed paths are those which the angular momentum is quantized by L=ħn and the electromagnetic radiation emission is only by transition through two of them
ν=(Ei-Ef)/h. I am asked to use the above assumptions to calculate the energy levels and the frequencies of transitions in a single electron atom. I am then asked to show that in the limit of high quantum numbers the result reduces to the classical one (the correspondence principle).

Homework Equations

The Attempt at a Solution

I managed to arrive at the expected expression for the energy levels, however I am not sure I explicitly used all the assumptions as instructed. What I did was this:
V=-e²/r, |F|=-∇V=e²/r²=mv²/r, hence v²=e²/mr=(nħ/mr)²
E_n=1/2*mv²-e²/r=-e²/2r_n where r_n=n²ħ²/me²=-13.6/n²
Does this suffice? Does this after all meet the instructions?

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?