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

Question

The relation between the magnetic moment μ of a revolving electron around the nucleus with principal quantum number n is (A) μ propto n (B) μ propto (1/n2) (C) μ propto (1/n3) (D) μ propto n2

Tardigrade Admin · Accepted Answer

μ =IA=eν⋅ π r2=(e ω /2 π )× π r2=(v e/2 r)× r2=(v e r/2) ⇒ μ propto vr[∵ v propto (1/n)] ⇒ μ propto (1/n)× n2[r propto n2] ⇒ μ propto n

Q. The relation between the magnetic moment $μ$ of a revolving electron around the nucleus with principal quantum number $n$ is

$μ \propto n$

$μ \propto \frac{1}{n ^{2}}$

$μ \propto \frac{1}{n ^{3}}$

$μ \propto n^{2}$

$μ = I A = e ν \cdot π r^{2} = \frac{e ω}{2 π} \times π r^{2} = \frac{v e}{2 r} \times r^{2} = \frac{v er}{2}$
$\Rightarrow μ \propto v r [∵ v \propto \frac{1}{n}]$
$\Rightarrow μ \propto \frac{1}{n} \times n^{2} [r \propto n^{2}]$
$\Rightarrow μ \propto n$

Q. The relation between the magnetic moment μ of a revolving electron around the nucleus with principal quantum number n is

μ∝n

μ∝n21​

μ∝n31​

μ∝n2