Question

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

• A. 8.8 x ${10}^{-12}$ C $k{g}^{-1}$
• B. 8.8 x ${10}^{10}$ C $k{g}^{-1}$
• C. 1.6 x ${10}^{-19}$ C $k{g}^{-1}$
• D. 6.67 x ${10}^{11}$ C $k{g}^{-1}$

Answer 1

The correct option is B 8.8 x ${10}^{10}$ C $k{g}^{-1}$

The gyromagnetic ratio is constant.
For any charged particle its value is given by
$\frac{{\mu }_l}{l}=\frac{e}{2m}$

For electron m = $m_e$ = 9.1 X ${10}^{-31}$kg, e = 1.6 X ${10}^{-19}C$,

$\therefore$ $\frac{{\mu }_l}{l}$ =$\frac{1.6\times {10}^{-19}}{2\times 9.1\times {10}^{-31}}=8.8\times {10}^{10}Ck$$g^{-1}.$