Question

The magnetic moment of an electron (e) revolving in an orbit around the 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 due to the orbital motion of an electron is proportional to the orbital angular momentum and inversely proportional to the mass of the electron.

Answer 1

The Correct Option is A

Step 1: The magnetic moment \( \vec{\mu}_L \) associated with the orbital angular momentum \( \vec{L} \) of an electron is given by the equation: \[ \vec{\mu}_L = \frac{e\vec{L}}{2m} \] where: \( e \) is the charge of the electron, \( \vec{L} \) is the orbital angular momentum (a vector), \( m \) is the mass of the electron. 
Step 2: Explanation of the formula. The electron in motion generates a magnetic field, and the magnetic moment is proportional to its orbital angular momentum. The factor \( \frac{1}{2m} \) arises from the relation between the electron’s angular momentum and the induced magnetic moment in orbital motion. 
Step 3: Verifying the correct answer. Thus, the correct expression for the magnetic moment is \( \vec{\mu}_L = \frac{e\vec{L}}{2m} \), which matches option (A).