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

Answer

A

Explanation

`T^(2) prop R^(3) and r prop n^(2) implies T^(2) prop n^(6) implies T prop n^(3)`
`(T_(1))/(T_(2)) = ((n_(1))/(n_(2)))^(3) implies 8 = ((n_(1))/(n_(2)))^(3) or (n_(1))/(n_(2)) = 2`
Only a satisfies the above, hence this is right choice.