An electron in the ground state of hydrogen atom is removing in unanticlockwise direction in a circle orbit of radius `R`

a. Obtain an expression for the orbital magnetic dipole moment of the electron .
b. The atom is placed in a uniform magnetic indution `bar B` such that the plane normal to the electron orbitmakes an angle of `30^(@)` with the magnetic induction. Find the tarque experienced by the orbiting electron .

Answer

A, B, C, D

Explanation

(i)In ground state `(n=1)`,according to Bohr's theory:
`mVR=j/(2pi)` or `V=h/(2pimR)`
Now time period,`T=(2piR)/V=(2piR)/(h//2pimR)=(4pi^(2)mR^(2))/h`
and `A=piR^(2)`
`:. M=(piR^(2))((eh)/(4pi^(2)mR^(2)))`
or `M=((eh)/(4pim))`
Direction of magnetic moment `vecM` is perpendicular to the plane of orbit
(b)`vectau=vecMxxvecBr` or `tau=MB sin theta`
where `theta` is the angle between `vecM` and `vecB rArr theta =30^(@)`
`:. tau=((eh)/(4pim))(B)sin 30^(@) rArr :. tau=(ehB)/(8pim)`
The direction of `vectau` is perpendicular to both `vecM` and `vecB`.