Solving the Math for D-Lines in Sodium Spectrum

[Mjolnir]

Homework Statement

I'm having some trouble working out the math for the D-lines in the sodium spectrum. Now the measured wavelengths are 5889.96 angstroms and 5895.93 angstroms. It's easy enough to find the energy difference between these to be .00213 eV. Now I'm supposed to be able to figure out the strength of the atomic magnetic field from here, but the class I'm in has really gotten to be over my head recently and I haven't been able to keep up with all the math/formulas

Homework Equations

the potential energy of a dipole in a field is given by -$$\mu$$*B.

The Attempt at a Solution

honestly don't know what I'm doing here. I found the energy difference I need to arrive at, as stated above, but aside from that I'm starting to think that taking a quantum physics course for "fun" probably wasn't the best move.

 

[Gokul43201]

Do not fret - you are on the right track. You have the equation for the interaction energy between a magnetic moment and a B-field. The splitting of the Na D-lines can be thought of as resulting from the tiny interaction between the moments of the oppositely "spinning" electrons and an effective B-field. The spin up and spin down electrons have opposite moments, and hence the interaction energies have opposite signs. So the difference (the splitting energy) is just twice the magnitude of each interaction term.

You need to know how to calculate the (spin) magnetic moment of an electron (it is a simple formula involving a quantity known as the Lande g-factor and a fundamental constant called the Bohr Magneton). Once you have done this, you simply plug into the equation you have written above, and from that you can extract the splitting energy as described in the above paragraph.