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. $0.1\times 10^{-29}kg$
• C. $1.1\times 10^{-29}kg$
• D. $\frac{1}{11}\times 10^{-29}kg$

Answer 1

Answer: (D)

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