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 ML
Let us consider
r= radius of the orbit
v= velocity
e= charge of electron
m= mass of electron
Time period (T)=‌

‌ circumference ‌

‌ velocity ‌

=2πr∕v
Current(i) =‌

−e

T

=‌

−e

2πr v

=‌

−ev

2πr

The magnetic moment due to a current loop enclosing an area A is given by:
ML=iA=‌

−ev

2πr

×A=‌

−ev

2πr

×πr2 =‌

−erv

2

=‌

−merv

2m

L= Angular momentum = mvr
So, ‌‌ML=‌

−e

2m

L