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 _______.
- \(\frac12k\hbar^2\)
- \(\frac32k\hbar^2\)
- \(\frac34k\hbar^2\)
- \(2k\hbar^2\)
The Correct Option is B
Solution and Explanation
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