According to Bohr's theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the `n^(th)` orbit is proportional to :
(n = principal quantum number)

Options

A. `1//n^3`
B. `1//n^5`
C. `n^5`
D. `n^3`

Answer

B

Explanation

The revolving electron is equivalent to current
`I=q/t`
But for the electron , q=e and
`t=T = (2pir)/(v) therefore I=(e )/((2pir)/(v)) = (ev)/(2pir)`
the field at the centre of the coil `=(mu_0)/(4pi) (2piI)/(r )`
or `F prop 1/r i.e. F prop (ev)/(2pirxxr) " or " F prop (v)/(r^2)`
`(therefore (e )/(2pi)` is a constant )
But in Bohr's model `v prop 1/n`
where n is the quantum number of the orbit and ` r prop n^2`
But `F prop (v)/(r^2)`
`therefore f prop (1)/(n(n^2)^2) therefore F prop 1/n^5`