What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition `n = 4` to `n=2` of ` He^(o+)` spectrum?

Explanation

For ` He^+ : 1/ (lambda) = R _H xx Z^2 [1/n_1^2 - 1/n_2^2]`,
` 1/ (lambda)R_H xx 4 [ 1/2^2 - 1/4^2 ] ( :. Fo r He Z=2) …(1)`
For H -atom `: (1)/ (lambda)R_H [1/n_1^2 - 1/n_2^2]` …(2)
For same ` (lambda)`,by eqs. (1) and (2),
` therefore 2^2 [ 1/2^2 - 1/4^2] = [ 1/n_1^2 - 1/n_2^2] , [ 1/1^2 - 1/2^2] = [ 1/n_1^2 - 1/n_2^2] `
`therefore n_1 = 1 "and " n_2 =2`.