A gyromagnetic ratio of the electron revolving in a circular orbit of hydrogen atom is $8.8\times {10}^{10}\mathrm{C}{\mathrm{kg}}^{-1}$ What is the mass of the electron? Given, charge of the electron $=1.6\times {10}^{-19}\mathrm{C}$
 

We know that Magnetic moment $M=iA$
$\text{ Where, }i=\frac{ev}{2\pi r},A=\pi r^2\mathrm{\&}M=\frac{ev}{2\pi r}\times \pi r^2\Rightarrow M=\frac{\text{ evr }}{2}$ and angular momentum Dividing Eq. (i) by Eq. (ii), we get
$\frac{M}{L}=\frac{e}{2m}\text{ where }\mathrm{M}/\mathrm{L}=$gyromagnetic ratio.
$\text{ Given, }\frac{M}{L}=8.8\times {10}^{10}\mathrm{C}/\mathrm{kg},e=1.6\times {10}^{-19}\mathrm{C}$
$m=\frac{e}{2\left(\frac{M}{L}\right)}=\frac{1.6\times {10}^{-10}}{2\times 8.8\times {10}^{10}}=\frac{8}{88}\times {10}^{-29}=\frac{1}{11}\times {10}^{-29}\mathrm{kg}$