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: Formula
The orbital magnetic moment is given by $\mu_l = \frac{e}{2m} L$, where $L$ is angular momentum.

Step 2: Analysis
According to Bohr's second postulate, $L = \frac{nh}{2\pi}$.

Step 3: Calculation
Substituting $L$, we get $\mu_l = \frac{e}{2m} \left( \frac{nh}{2\pi} \right) = n \left( \frac{eh}{4\pi m} \right)$.

Step 4: Conclusion
Since $\frac{eh}{4\pi m}$ is a constant (Bohr Magneton), $\mu_l \propto n$. Final Answer: (A)