In the Bohr model an electron moves in a circular orbit around the proton. Considering the orbiting electron to be a circular current loop, the magnetic moment of the hydrogen atom, when the electron is in nth excited state, is :

Options

A. `((e)/(2m))(n^(2)h)/(pi)`
B. `((e)/(m))(nh)/(2pi)`
C. `((e)/(2m))(nh)/(2pi)`
D. `((e)/(m))(n^(2)h)/(2pi)`

Answer

C

Explanation

As, `i=(e)/(T)` and magnetic moment `M=iA" "(because a=pir^(2))`
`therefore M=(e)/(T)*pir^(2)` . . . (i)
Now, `T=(2pir)/(v)`
it becomes, `M=((e)/(2pir)*pir^(2))/(v)=(evr)/(2)=(evr)/(2)` . . . (ii)
Also, `mvr=(nh)/(2pi),vr=(nh)/(2pim)`
Putting this value in Eq. (ii), we get
`M=(e*nh)/(2*2pim)=((e)/(2m))(nh)/(2pi)`