# Orbital Spin and External Magnetic Fields

1. Nov 12, 2009

### ourio

1. The problem statement, all variables and given/known data
A Hydrogen atom is subjected to a magnetic field strong enough to overwhelm the spin-orbit coupling. Into how many levels would the 2p level split? What would the spacing be in the terms of Bext, e, me, and $$\hbar$$

2. Relevant equations
I know that I have to use the gLande equation:
U=gLande$$\frac{e}{2(me)}$$mj$$\hbar$$Bext

3. The attempt at a solution
I have a feeling that the 2p level will split into 3 levels, but I honestly don't know how to show it.

Any help will be greatly appreciated!

2. Nov 12, 2009

### ourio

OK... I think I may have got some of it....
The 2p state of hydrogen has $$\ell$$=1 with m$$\ell$$=-1,0,1
So the 2p state splits into three levels by the external B.

Calculating the gLande factor for the 2p state as $$\frac{4}{3}$$ and the 1s state as 2, I find that the splitting of the 2p state is only $$\frac{2}{3}$$ that of the 1s state

SO... the spacing between the levels is:
$$\frac{e\hbar}{2m}$$Bext$$\frac{2}{3}$$

Does that look right to anybody out there??? Help! :-(