How Is Frequency Calculated in the Stern-Gerlach Experiment?

[erok81]

Homework Statement

I have a Stern-Gerlach experiment with a beam of silver and a magnetic moment due to the spin of the single valence electron give by μ=e/m_e S. And |S|=ℏ/2. The magnetic field is 1T.

The problem asks to compute the energy difference of the silver atoms in the two existing beams. The second part - which I am really confused on - Next up I am to find the frequency of the radiation that would induce a transition between these two states.

Homework Equations

The Attempt at a Solution

The energy of each beam is U=μ_s·B

Hence the energy is

$$E=\pm \frac{1}{2} \hbar \frac{e}{m_e} g B$$

Therefore ΔE is

$$E= \frac{1}{2} \hbar \frac{e}{m_e} g B ~+~ \frac{1}{2} \hbar \frac{e}{m_e} g B~=~ \hbar \frac{e}{m_e}$$

Where g≈2 and B=1 so there is a little cancelling.

My units end up being N·m = J.

I am worried this is wrong. My answer is really close to the Bohr Magneton. It is off by a 2 in the denominator and my units aren't quite right. So I guess first off, did I proceed correctly so far?

If that is correct, how does one even begin the second half? With no quantized energies I don't know where to start.

 

[member 553083]

I'm assuming it involves the energy difference, but I'm not sure. Any help would be greatly appreciated!