Question

The orbital magnetic moment \((m_{orb})\) of a revolving electron around the nucleus varies with the principal quantum number (\(n\)) as

• A. \(m_{orb}\propto n^2\)
• B. \(m_{orb}\propto n\)
• C. \(m_{orb}\propto \frac{1}{n^2}\)
• D. \(m_{orb}\propto \frac{1}{n}\)

Hint:

\(m_{orb}=\dfrac{e}{2m}L\) with \(L=\dfrac{nh}{2\pi}\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
For an electron in orbit, the magnetic moment is \(m_{orb}=\dfrac{e}{2m_e}L\), where \(L\) is the orbital angular momentum.

Step 2: Key Formula or Approach
In Bohr's model, \(L=\dfrac{nh}{2\pi}\).

Step 3: Detailed Explanation
\[ m_{orb}=\frac{e}{2m_e}\cdot\frac{nh}{2\pi}=n\,\frac{eh}{4\pi m_e} \]
So \(m_{orb}\propto n\).

Final Answer:
The magnetic moment is proportional to \(n\), option (B). \[ \boxed{m_{orb}\propto n\ \text{(B)}} \]