GATE 2025 PH – Question 24

Atomic and Molecular Physics · fine and hyperfine structures · 1 mark · Multiple select

Which of the following option(s) is/are correct for the ground state of a hydrogen atom?

Show answer and explanation

Correct answer: (A) Linear Stark effect is zero; (B) It has definite parity; (C) Spin-orbit coupling is zero

Explanation

Check each statement for the ground state (1s) of hydrogen.

**A. The linear Stark effect is zero.** True. The 1s state has no permanent electric dipole moment (it is non-degenerate and has definite parity), so there is no first-order energy shift in an electric field; only the quadratic Stark effect appears. ✓
**B. It has definite parity.** True. The 1s wave function is spherically symmetric, so it is even. ✓
**C. Spin-orbit coupling is zero.** True. For $l=0$ the orbital angular momentum is zero, so $\mathbf L\cdot\mathbf S=0$. ✓
**D. Hyperfine splitting is zero.** False. The coupling of the electron spin to the proton spin splits the 1s level into $F=0$ and $F=1$ (the 21 cm line).

Answer **A, B and C**.