# Derivation of the Bohr Magneton

1. Oct 3, 2004

### aeroegnr

This is a homework problem, and I already turned in the wrong answer (on purpose because I didn't agree with the explanation of why the correct answer was twice mine). I want to know why the answer is what it is. The stated book value is 9.274009 x 10^-24 J/T. I got exactly half that, and I know the equations that the official solution used.

The question is stated thus:
a) the current i due to a charge q moving in a circle with frequency f_rev is q*f_rev. Find the current due to the electron in the first bohr orbit.

So, what I did was I used the equation h*f=E, where E was the energy of the first orbit in hydrogen, which was 13.6eV. (I know that this is where I made the mistake) I then computed the current that way and got 9.274.../2 as the answer. The book solution manual, which I do not trust because it offers no explanation, used this equation:

f~Z^2*m*k^2*e^4/(2*pi*h_bar^3*n^3) and plugged in the value of n=1 to get the frequency.

however, the above equation is an approximation for large n. The actual equation that the above is derived from is:

Z^2*m*k^2*e^4/(4*pi*h_bar^3) * (2n-1)/(n^2*(n-1)^2)

I know that for large n, this equation approaches the other one they used. However, they plugged in the value of 1 into the approximation, when the real answer would have been undefined (divide by 0)!

I was told by the professor that I could use the equation f=v/(2pi*r), which did not suit me because you end up with the approximation equation above.

What am I confused about here?

2. Oct 4, 2004

### theFuture

Well, if the book is using the approximation and you are only off by a factor of two my guess is that you are fine. You work seems fine.