Question

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

• A. $1\times {10}^{-29}kg$
• B. $0.11\times {10}^{-29}kg$
• C. $1.1\times {10}^{-29}kg$
• D. $\frac{1}{11}\times {10}^{-29}kg$

Answer 1

The correct option is D $\frac{1}{11}\times {10}^{-29}kg$

Magnetic moment $\mu =evr/2$

Angular momentum $L=mvr$

Gyromagnetic ratio is the ratio of magnetic moment of the particle to its angular momentum.

$\therefore$ $\gamma =\frac{\mu }{L}=\frac{evr/2}{mvr}$

$⟹$ $\gamma =\frac{e}{2m}$

Or $8.8\times {10}^{10}=\frac{1.6\times {10}^{-19}}{2m}$

$⟹$ $m=\frac{1}{11}\times {10}^{-29}$ $kg$