What is the moment of inertia of the electron moving in second Bohr orbit of a hydrogen atom ?

Options

A. `(4epsi_0^2h^4)/(pi^2me^4)`
B. `(8mepsi_0^2h^4)/(pi^2 e^4)`
C. `(16 epsi_0^2 h^4)/(pi^2 me^4)`
D. `(epsi_0^2 h^4)/(16pi^2me^4)`

Answer

C

Explanation

`I=mr^2`
The radius fo the nth Bohr orbit of an electron in a hydrogen atom is given by
`r_n = (epsi_0 h^2 n^2)/(pime^2) " for " n =2, r_2 = (4epsi_0h^2)/(pime^2)`
`therefore M.I. (I) = mr_2^2`
`=m.[(16epsi_0^2h^4)/(pi^2m^2e^4)] = (16epsi_0^2h^4)/(pi^2me^4)`