The electron in a hydrogen atom make a transtion `n_(1) rarr n_(2)` where `n_(1) and n_(2)` are the priocipal quantum number of the two states . Assume the Bohr model to be valid . The time period of the electron in the initial state is eight time 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)`