The electron in a hydrogen atom makes a transition `n _(1) to n _(2)` where `n_(1) and n_(2)` are the principal quantum numbers of the two states. Assume the Bohr model to be valid. The frequency of orbital motion of the electron in the initial state is `(1)/(27)` of that in the final state. The possible values of `n_(1) and n_(2)` are

Options

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

Explanation

`T alpha n ^(3)`
`(T_(i))/( T _(f) ) = (1)/( 27) = ((n _(i))/( n _(2))) ^(3) implies (n _(1) )/( n _(2)) = (1)/(3)`