Question

A gyromagnetic ratio of the electron revolving in a circular orbit of hydrogen atom is $8.8 \times 10^{10}\, C\, kg^{-1}$. 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 $i=\frac{e v}{2 \pi r}$
$A=\pi r^{2}$
$M=\frac{e V}{2 \pi r} \times \pi r^{2}$
$M=\frac{e V r}{2}$...(i)
and angular momentum
$L= mvr$...(ii)
Dividing Eq. (i) by Eq. (ii), we get
$\frac{M}{L}=\frac{e}{2 m}$
where $M / L=$ gyromagnetic ratio.
Given,
$\frac{M}{L} =8.8 \times 10^{10} C / kg$
$e =1.6 \times 10^{-19} C$
$\therefore m =\frac{e}{2\left(\frac{M}{L}\right)}$
$=\frac{1.6 \times 10^{-19}}{2 \times 8.8 \times 10^{10}}$
$=\frac{8}{88} \times 10^{-29}$
$=\frac{1}{11} \times 10^{-29} kg$