Question

The spin-orbit interaction in a hydrogen-like atom is given by the Hamiltonian $H' = -k \vec{L} \cdot \vec{S}$, where $k$ is a real constant. The splitting between levels $^2P_{3/2}$ and $^2P_{1/2}$ due to this interaction is _______.

• A. $\frac12k\hbar^2$
• B. $\frac32k\hbar^2$
• C. $\frac34k\hbar^2$
• D. $2k\hbar^2$

Answer 1

Answer: (B)

$\frac32k\hbar^2$

Answer 2

The correct option is (B) :$\frac32k\hbar^2$