Calculate the wavelength emitted during the transition of an electron in between two level of `Li^(2+)` ion whose sum is `4` and difference is `2`.

Explanation

Suppose the transition takes place between two levels `n_1` and `n_2` and
`n_2 - n_1 = 2 " "….(i)`
and `" " n_2 + n_1 = 4 " " ……(ii)`
In order to solve for the values of `n_1 and n_2` , add eqn (i) and (ii)
`2n_2 = 6 " or " n_2 = 3`
and `3 - n_1 = 2 " or " n_1 = 1`
According to Rydberg equation
`1/lambda = R (1/(n_1^2) - 1/(n_2^2))Z^2`
For `Li^(2+), Z = 3, R = 109677 cm^(-1)`
`1/lambda = 109677 (1/(1^2) -1/(3^2)) xx 3^2`
`= 109677 (1/1 - 1/9) xx 9`
`= 109677 xx 8/9 xx 9`
`1/lambda = 109677 xx 8 cm^(-1) = 877416 cm^(-1)`
or `lambda = 1/(877416 cm^(-1)) = 1.14 xx 10^(-6) cm`
or `lambda = 1.14 xx 10^(-8) m "or" 11.4 nm`