Question

Gyromagnetic ratio is the ratio of magnetic moment $(\mu_{1})$ to the orbital angular momentum $(l)$ Its numerical value for an electron is given by

• A. $8.8 \times 10^{-12}\,C\, kg^{-1}$
• B. $8.8 \times 10^{10}\,C\, kg^{-1}$
• C. $1.6 \times 10^{-19}\,C\, kg^{-1}$
• D. $6.67 \times 10^{11}\,C\, kg^{-1}$

Answer 1

Answer: (B)

The gyromagnetic ratio is a constant.
For any charged particle its value is given by
$\frac{\mu_{l}}{l}=\frac{e}{2m}$
For electron $m=m_{e}=9.1 \times 10^{-31}\, kg$,
$e=1.6 \times 10^{-19}\, C$,
$\therefore \frac{\mu_{l}}{l}=\frac{1.6\times10^{-19}}{2\times9.1\times10^{-31}}$
$=8.8\times10^{10}\,C \,kg^{-1}$