Among the following, which transition in the hydrogen spectrum would have the same wavelength as Balmer transition, n=4 to n=2 in He ⁺ spectrum?

Step-by-step solution

We know that, 1 =R_ H Z^2 [ 1 n₁^2 - 1 n₂^2 ] For He ,(Z=2) 1 _ He =R_ H (2)^2 [ 1 2^2 - 1 4^2 ]=R_ H 4 [ 1 4 - 1 16 ]=R_ H 4 3 16 1 _ He = 3 4 R_ H For option (d), n=1 and n₂=2 1 _ H = R_ H 1 [ 1 1^2 - 1 2^2 ]= 3 4 R_ H So, option (d) is correct.