Question

The relation between the magnetic moment $\mu $ of a revolving electron around the nucleus with principal quantum number $n$ is

• A. $\mu \propto n$
• B. $\mu \propto \frac{1}{n^{2}}$
• C. $\mu \propto \frac{1}{n^{3}}$
• D. $\mu \propto n^{2}$

Answer 1

Answer: (A)

$\mu =IA=e\nu\cdot \pi r^{2}=\frac{e \omega }{2 \pi }\times \pi r^{2}=\frac{v e}{2 r}\times r^{2}=\frac{v e r}{2}$
$\Rightarrow \mu \propto vr\left[\because v \propto \frac{1}{n}\right]$
$\Rightarrow \mu \propto \frac{1}{n}\times n^{2}\left[r \propto n^{2}\right]$
$\Rightarrow \mu \propto n$