Calculate the ratio of the frequencies of the radiation emitted due to transition of the electron in a hydrogen atom from its (i) second permitted energy level to the first level, and (ii) highest permitted energy level to the second permitted level.

Explanation

We know that frequency of radiation emitted due to transition of an electron in a hydrogen atom from n state to n, stale is given by
`v = (13.6 e)/(h) [(1)/(n_(j)^(2))-(1)/(n_(i)^(2))]`
For 2-1 transition (i.e., `n_(i) = 2` and `n_(j) = 1`) we , have
`V = (13.6e)/(h) [(1)/((1)^(2)) - (1)/((2)^(2))] = (3)/(4) xx (13.6e)/(h)" ".......(i)`
For n - 2 transition (i.e., `n_(i) = oo ` and `n_(j) = 2`) we have .
`v = (13.6e)/(h) [(1)/((2)^(2)) - (1)/((oo)^(2))] = (1)/(4) xx (13.6 e)/(h)`
`rArr" "(v)/(v) = (3)/(1) or v = 3 v`