A particular hydrogen like radiation of frequency `2.467 xx 10^(15)Hz` when it makes transition from `n = 2 to n = 1` ,What will be the frequency of the radiation emitted in a transition from `n = 3 to n= 1`?

Explanation

The frequency of radiation emitted is given by
`v = ©/(lambda) = K((1)/(n_(1)^(2))- (1)/(n_(2)^(2)))`
Thus `2.467 xx 10^(15) Hz= K((1)/(1^(2)) - (1)/(2^(2)))`
or` K = (4)/(3) xx 2.467 xx 10^(15) Hz`
The frequency of the radiation emitted in the transition
`n = 3 to n= 3` is
`v^(1) = K[(1)/(1^(2)) - (1)/(3^(2))]`
` = (8)/(9)K= (8)/(9)2.467 xx 10^(15) Hz`
` = 2.92 xx 10^(15)Hz`.