The rartio `("in SI units")` of magnetic dipole moment to that of the angular momentum of an electron of mass `m kg` and charge `e` coulomb in Bohr's orbit of hydrogen atom is

Options

A. `e/m`
B. `m/e`
C. `(2m)/(e)`
D. `(e)/(2m)`

Answer

D

Explanation

Angular momentum, `L=m_(e)vr` . (i)
Therefore, orbital motion of electron is equivalent to a current, `i=e(1//T)`
Period of revolution of electron is given by
`T=(2pir)/(v)`
`therefore l=e((1)/(2pir//v))=(ev)/(2pir)`
Area of electron orbit, `A=pir^(2)`
Magnetic dipole moment of the atom
`M=(ev)/(2pir)xxpir^(2)=evr`
Using eq. (i) we have `M=((e)/(2m_(e)))L`