What is the gyromagnetic ratio? Give its magnitude.

The gyromagnetic ratio is defined as the ratio of the magnetic dipole moment $(M)$ of an electron to its angular momentum $(L)$.
Mathematically,it is expressed as: $\gamma = \frac{M}{L}$.
For an electron revolving in a circular orbit,the magnetic moment is $M = \frac{evr}{2}$ and the angular momentum is $L = mvr$.
Therefore,$\gamma = \frac{evr/2}{mvr} = \frac{e}{2m}$.
Substituting the values of the charge of an electron $(e \approx 1.6 \times 10^{-19} \ C)$ and the mass of an electron $(m \approx 9.1 \times 10^{-31} \ kg)$,the magnitude is:
$\gamma = \frac{1.6 \times 10^{-19}}{2 \times 9.1 \times 10^{-31}} \approx 8.8 \times 10^{10} \ C/kg$.