In a hydrogen atom, the electron moves in an orbit of radius  $0.5\stackrel{0}{A},$ making ${10}^{16}$ rps Calculate the magnetic moment associated with the orbital motion of electron.

Here,  $r=0.5\stackrel{0}{A}=0.5\times {10}^{-10}m,v={10}^{16}\text{rps}$

M=?

Charge on electron, $e=1.6\times {10}^{-19}\mathrm{C}$

Equivalent current,  $I=\frac{e}{T}=ev$    $\left[\because v=\frac{1}{T}\right]$

Area of the orbit

$A=\pi r^2\Rightarrow M=IA$

$M=ev\left(\pi r^2\right)$

$=1.6\times {10}^{-19}\times {10}^{16}\times 3.14\times {(0.5\times {10}^{-10})}^2$

$M=1.256\times {10}^{-23}{\mathrm{Am}}^2$