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 ${ }^{2} P$.