Excited sodium atoms emit two closely spaced spectrum lines called the sodium doublet (Fig. 40-27) with wavelengths

Question:

Excited sodium atoms emit two closely spaced spectrum lines called the sodium doublet (Fig. 40-27) 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 electron's spin magnetic moment can be oriented either parallel or anti-parallel 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.