Question

The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given by:

• A. \( \vec{\mu}_L = \frac{e \vec{L}}{2m} \)
• B. \( \vec{\mu}_L = -\frac{e \vec{L}}{2m} \)
• C. \( \vec{\mu}_l = -\frac{e \vec{L}}{m} \)
• D. \( \vec{\mu}_l = \frac{2e \vec{L}}{m} \)

Hint:

The magnetic moment of a particle moving in a circular orbit is given by \( \vec{\mu}_L = -\frac{e \vec{L}}{2m} \), where the negative sign accounts for the negative charge of the electron.

Answer 1

The Correct Option is B

Step 1: The magnetic moment of an electron moving in a circular orbit is related to its orbital angular momentum by the equation: \[ \vec{\mu}_L = -\frac{e \vec{L}}{2m}. \] Step 2: The negative sign indicates that the direction of the magnetic moment is opposite to the direction of the angular momentum due to the negative charge of the electron.