Find an expression fot the magneitc dipole moment and magnetic field induction at the centre of Bohr'r hypothetical hydrogen atom in the n th orbit of the electron in terms of universal constant.

Answer

B, D

Explanation

Magnetic moment, `mu = NiA = ((e )/(T) (pir^2)`
or `mu = (e )/(2pir//v) (pir^2) = (evr)/(2) …(i)`
We know that `mvr = (nh)/(2pi) …(ii)`
Solving Eqs. (i) and (ii) we get
`mu = (neh)/(4pim)`
`Megnetic induction, B = (mu_0i)/(2r) = (mu_0e)/(2rT)`
or `B = (mu_0eV)/(2r)(2pir) =(mu_0eV)/(4pir^2) .....(iii)`
From Newton's second law,` (e^2)/(4piepsilon_0r^2) = (mv^2)/(r)`
or `v^2 = (e^2)/(4pi epsilon_mr)/(8epsilon_0h^5n^5).`