Calculate the wavelength of the spectral line obtained in the spectrumof Li^(2+) ion when the transition takes place between two levels whose sum is 4 and the difference is 2

Calculate the wavelength of the spectral line obtained in the spectrum

1.	Calculate the wavelength of the spectral line obtained in the spectrumof Li^(2+) ion when the transition takes place between two levels whose sum is 4 and the difference is 2
Answer» Solution :Suppose the transition takes place between LEVELS `n_(1) and n_(2)` Then `n_(1) + n_(2) = 4 and n_(2) - n_(1) = 2` SOLVING these equations, we get `n_(1) = 1, n_(2) = 3 :. (1)/(lamda) = R ((1)/(n_(1)^(2)) - (1)/(n_(2)^(2))) Z^(2)` For `LI^(2+) , Z = 3 :. (1)/(lamda) = 109, 677 cm^(-1) ((1)/(1^(2)) - (1)/(3^(2))) xx 3^(2) = 109, 677 xx ((1)/(1) - (1)/(9)) xx 9 cm^(-1) = 109677 xx 8 cm^(-1)` or `lamda = (1)/(109677 xx 8 cm^(-1)) = 1.14 xx 10^(-6) cm`