An electron in a hydrogen atom makes a trsnsition `n_(1)rarrn_(2)` where `n_(1)` and `n_(2)` are principal quantum numbers of the two states. Assume the Bohr model to be valid. The time period of the electron in the initial state is eight times that in the final state. The possible values of `n_(1)` and `n_(2)` are

Options

A. `n _(1) = 6, n _(2) = 3`
B. `n _(1) = 4, n _(2) = 2`
C. `n _(1) = 8, n _(2) = 1`
D. `n _(1) = 3, n _(2) = 1`

Answer

D

Explanation

We know that that frequency of orbital motion
`f prop (1)/(n^(3)) and given f_(1) = (1)/(27) f_(2)`
implies `((n_(2))/(n_(1))^(3) implies (f_(1))/f_(2)) implies (n_(2))/(n_(1))^1//3 = (1)/(3)`