Orbital motion electron (quantum)

[hvthvt]

Homework Statement

Excited sodium atoms emit two closely spaced spectrum lines called the sodium doublet with wavelengths 588.995 nm and 589.592 nm. (a) What is the difference in energy between the two upper energy levels (n=3 l=1)? (b) This energy difference occurs because the electrons spin magnetic moment can be oriented either parallel or antiparallel to the internal magnetic field associated with the electron's orbital motion. Use your result in (a) to find the magnitude of this internal magnetic field

Homework Equations

E=hf=hc/λ

Orbital motion: =−(e*L)/2m (Is the e in this formula 1.602*10^-19?)

The Attempt at a Solution

For (a), I think the energy difference is simply caused by the difference in wavelength: which is 0.597 nm. E=hc/λ gives E=3.3*10^-16 J. Is this correct?
However, for the second part (b), I don't really know how to tackle the problem.
E=μ(orb)*B
So B=E/μ i guess. To know what μ is, first I should determine L: which is (√(l(l+1)))*h/2π
Can anybody tell me if I'm working in the right way?
L=1.49*10^-34
so μ=-1.31*10^-23?
Giving B=2.5*10⁷
Is this correct?

 

[hvthvt]

Hmm, I see they ask INTERNAL magnetic field. Now it just crossed my mind that I remember something as
B_total=B_int+B_ext
Is this true? What should I do with it? Does that mean that Bint is just the half of Btotal?

 

[nasu]

First, the energy difference is not right.
If E1=hc/λ1 and E2=hc/λ2, the difference E1-E2 is NOT hc/Δλ.

Then they are talking about the magnetic moment associated with the electron's spin, aren't they?
What is the spin magnetic moment? It is not calculated by using the orbital quantum number.

And there is no external field. "Internal" here means produced by the orbital motion of electrons in the atom.