\(\bar v=\frac{1}{λ}= R_H\Big[\frac{1}{n^2_1}-\frac{1}{n_2^2}\Big]\)
Longest wavelength n1 = 2 and n2 = 3
\(=\frac{1}{λ}= R_H\Big[\frac{1}{n^2_1}-\frac{1}{n_2^2}\Big]\) \(R_H\Big[\frac{1}{2^2}-\frac{1}{3^2}\Big]\)
λ = \(\frac{1}{R_H\Big[\frac{1}{2^2}-\frac{1}{3^3}\Big]}\) = 6563 A0
Shortest Wavelength n1 = 2 and n2 = α
\(=\frac{1}{λ}= R_H\Big[\frac{1}{n^2_1}-\frac{1}{n_2^2}\Big]\) = \(R_H\Big[\frac{1}{2^2}-\frac{1}{\alpha^2}\Big]\)
λ =\(\frac{1}{R_H\Big[\frac{1}{2^2}-\frac{1}{\alpha^2}\Big]}\) = \(\frac{1}{1.097\times10^7\Big(\frac{1}{4}\Big)}\)
= 3646 A0