Question

An electron in the ground state of hydrogen atom is revolving in a circular orbit of radius \(R\). The orbital magnetic moment of the electron is (\(m\) = mass of electron, \(h\) = Planck’s constant, \(e\) = electronic charge)

• A. \( -\dfrac{eh}{\pi m} \)
• B. \( \dfrac{eh}{2\pi m} \)
• C. \( \dfrac{2eh}{\pi m} \)
• D. \( \dfrac{eh}{4\pi m} \)

Hint:

Orbital magnetic moment is directly proportional to angular momentum.

Answer 1

The Correct Option is D

Step 1: Expression for orbital magnetic moment.
Orbital magnetic moment of an electron is \[ \mu = \frac{e}{2m}L, \] where \(L\) is orbital angular momentum.
Step 2: Angular momentum in ground state.
For ground state, \[ L = \frac{h}{2\pi}. \]
Step 3: Substitution.
\[ \mu = \frac{e}{2m}\cdot\frac{h}{2\pi} = \frac{eh}{4\pi m}. \]
Step 4: Conclusion.
The orbital magnetic moment is \( \dfrac{eh}{4\pi m} \).