Question

An electron (\( e \)) is revolving in a circular orbit of radius \( r \) in a hydrogen atom. The angular momentum \( M \) of the electron is
\textit{(where \( M \) = magnetic dipole moment associated with it and \( m \) = mass of the electron)}

• A. \( \frac{4mM}{e} \)
• B. \( \frac{2mM}{e} \)
• C. \( \frac{3mM}{e} \)
• D. \( \frac{mM}{e} \)

Hint:

For hydrogen atoms, the angular momentum is quantized and related to the magnetic dipole moment.

Answer 1

The Correct Option is B

Step 1: Angular momentum in the hydrogen atom.
The angular momentum \( L \) of an electron in a hydrogen atom is quantized and given by: \[ L = \frac{nh}{2\pi} \] where \( n \) is the principal quantum number and \( h \) is Planck’s constant. For the first orbit (\( n = 1 \)), the magnetic dipole moment \( M \) is related to angular momentum by: \[ M = \frac{eL}{2m} \] So, the angular momentum \( M \) is \( \frac{2mM}{e} \).
Step 2: Conclusion.
Thus, the correct answer is (B) \( \frac{2mM}{e} \).