Question

The magnetic moment $\left(\mu \right)$ of an electron revolving around the nucleus, varies with principal quantum number $n$ as,

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

Answer 1

The correct option is B $\mu \propto n$

Magnetic moment $\left(\mu \right)$ of a revolving electron around the nucleus varies with principle quantum number as,
${\mu }_n=\frac{eL}{2m}$
According to second postulate of Bohr's theory,
$L=\frac{nh}{2\pi }$

$\therefore \mu =\frac{enh}{4\pi m}$

Here, $e\to$ charge of an electron
$n\to$ principle quantum number
$h\to$ Planck's constant
$m\to$ mass of electron

So, we can write, $\mu \propto n$

Hence, $\left(\text{A}\right)$ is the correct answer.

Why this question ? This question is based on magnetic moment of an electron revolving around the nucleus and angular momentum of an electron in the $n^{\text{th}}$ orbit.