An electron in the ground state of hydrogen atom is revolving in anti-clockwise direction in the circular orbit of radius R as shown in figure.

Obtain an expression for the orbital magnetic dipole moment of the electron.

Explanation

According to Bohr's second postulate
`mvr =n "" ( h )/( 2pi ) = ( h )/( 2pi ) ` ( As for n =1 first only )
or `v_(1) = ( h )/( 2pi m r_(1))`
We know that the rate of flow of charge is current .Hence current in first orbit is
Now from each equation
`i = ev_(1) =e ((v_(1))/( 2pi r_(1))) = ( e )/( 2pi r_(1)) xx v_(1)`
`i = ( e)/( 2 pi r _(1)) xx( h ) /( 2pi n r_(1)) = ( eh )/( 4pi ^(2) mr^(2))`
Magnetic dipole moment, `M_(1) =i xx A_(1)`
or `M_(1) = ( eh)/( 4pi ^(2) m r^(2)) xx pi r_(1)^(2) = ( eh )/( 4pi m )`