In Bohr model of Hydrogen atom, electron is modeled as a point negative charge rotating in a circular orbit about a fixed axis about a nucleus. Magnetic moment $M_{L}$ Let us consider $r=$ radius of the orbit $v=$ velocity $e=$ charge of electron $m=$ mass of electron Time period $(T)=\frac{\text{ circumference }}{\text{ velocity }}=\frac{2\pi r}{v}$ Current(i) $=\frac{-e}{T}=\frac{-e}{\frac{2\pi r}{v}}=\frac{-e v}{2\pi r}$ The magnetic moment due to a current loop enclosing an area $A$ is given by: $M_{L}=iA=\frac{-e v}{2\pi r}\times A=\frac{-e v}{2\pi r}\times \pi r^{2}$ $=\frac{-e r v}{2}=\frac{-m e r v}{2m}$ $L=$ Angular momentum $=mvr$ So, $M_{L}=\frac{-e}{2m}L$