Problem 6.163

The wavelengths of the Na yellow doublet \(\left({ }^{2} P \rightarrow{ }^{2} S\right)\) are equal to 589.59 and \(589.00 \mathrm{nm} .\) Find: (a) the ratio of the intervals between neighbouring sublevels of the Zeeman splitting of the terms \({ }^{2} P_{3 / 2}\) and \({ }^{2} P_{1 / 2}\) in a weak magnetic field; (b) the magnetic field induction \(B\) at which the interval between neighbouring sublevels of the Zeeman splitting of the term \({ }^{2} P_{3 / 2}\) is \(\eta=50\) times smaller than the natural splitting of the term \({ }^{2} P\).