# Magnetic Moment and Spacing of Adjacent Magnetic Substates

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1. Nov 21, 2017

### njdevils45

1. The problem statement, all variables and given/known data

Consider the hydrogen atom in the 42F5/2 state. Take into account the effects of finestructure (spin-orbit coupling).
(a) Write down the spectroscopic notation of the state that the 42F5/2 is degenerate with, in the absence of an external magnetic field.
(b) Calculate the magnitude of the magnetic moment of the hydrogen atom in the 42F5/2 state, in units of the Bohr magneton µB.
(c) Suppose the hydrogen atom in the 42F5/2 state is placed in an external magnetic field B. What will be the spacing in energy between adjacent magnetic substates, in terms of µBB, where again µB is the Bohr magneton?

3. The attempt at a solution

So I actually managed to do all three of them. But the solutions I got for B and C were so simple I feel like I did something wrong like maybe used the wrong equation of forgot to add something.

A) Degenerate with 42D5/2

B) I said that j =5/2, l = 3, s = 1/2. With this info I found the lande g factor to be = 0.857
Then I used μJ = |ge√(j(j+1) ħ/2m = 0.857µB√(5/2(5/2+1) = 2.54µB

C) I said ΔE = ΔmjBB where Δmj = 1 between adjacent substates. So

ΔE = 0.857µBB

Was just hoping I could get a double check on these solutions and any tips if they were wrong.

2. Nov 22, 2017

### Staff: Mentor

I'm not sure what you are doing here. What equation is this based on?

The rest appears correct.

3. Nov 22, 2017

### njdevils45

I'm not sure. I just found this,

On the lecture slides.

I used the equation for "THE" Magnetic Moment, which I think takes into account fine structure. I think I just wasn't able to write it out using keyboard. Did I miss something or use the wrong equation?