Which of the following transitions of He ⁺ ion will give rise to spectral line which has same wavelength as the spectral line in hydrogen atom?

Step-by-step solution

Let the transition of electron in hydrogen atom (Z=1) gives wavelength ₁ for transition from n₂ to n₁ , then 1 =R Z^2 ( 1 m^2 - 1 n^2 ) Here, = ₁, Z=1, m=n₁, n=n₂ 1 ₁ =R(1)^2 ( 1 n₁^2 - 1 n₂^2 )=R ( 1 n₁^2 - 1 n₂^2 ) Now, if electron makes transition in He ⁺ ion from n₄ to n₃ and gives wavelength ₂ , then aligned 1 ₂ & =R(2)^2 ( 1 n₃^2 - 1 n₄^4 ) & =R [ 1 ( n₃ 2 )^2 - 1 ( n₄ 2 )^2 ] aligned Given that, ₁= ₂ R ( 1 n₁^2 - 1 n₂^2 )=R [ 1 ( n₃ 2 )^2 - 1 ( n₄ 2 )^2 ] On comparing beth sides, we get n₁= n₃ 2 and n₂= n₄ 2