Question

The orbital magnetic dipole moment of an electron in hydrogen-like atom is \( \sqrt{2} \mu_B \). What is the state of the electron?

• A. S
• B. P
• C. D
• D. F

Hint:

Magnetic dipole moment depends on the orbital angular momentum quantum number.

Answer 1

The Correct Option is C

The orbital magnetic dipole moment is given by:
\[ \mu_L = \sqrt{l(l+1)} \mu_B \] For \( \mu_L = \sqrt{2} \mu_B \):
\[ \sqrt{l(l+1)} = \sqrt{2} \] Solving for \( l \), we get \( l = 2 \), which corresponds to the D-state.