Question

The magnetic moment of electron due to orbital motion is proportional to ($n=$ principal quantum number)

• A. $n$
• B. $n^{2}$
• C. $1/n$
• D. $1/n^{3}$

Hint:

Magnetic moment increases linearly with the orbit number $n$.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the dependence of the orbital magnetic moment of an electron in a hydrogen-like atom on the principal quantum number \( n \).

Step 2: Key Formula or Approach:
The orbital magnetic moment (\( M \)) is related to the orbital angular momentum (\( L \)) by the relation \( M = \frac{e}{2m} L \).
According to Bohr's quantization rule, \( L = \frac{nh}{2\pi} \).

Step 3: Detailed Explanation:
Substitute the expression for \( L \) into the formula for \( M \):
\[ M = \frac{e}{2m} \left( \frac{nh}{2\pi} \right) \]
\[ M = \left( \frac{eh}{4\pi m} \right) n \]
The term in the bracket is the Bohr magneton (\( \mu_B \)), which is a constant.
Therefore, \( M \propto n \).

Step 4: Final Answer:
The orbital magnetic moment is directly proportional to \( n \).