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

Question 2.33: What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition n = 4 to n = 2 of He⁺ spectrum?
Answer

For He⁺ ion, the wave number associated with the Balmer transition, n = 4 to n = 2   the wave number is  given by:

Where,
n₁ = 2
n₂ = 4
Z = atomic number of helium

According to the question, the desired transition for hydrogen will have the same wavelength as that of He⁺.

By hit and trail method, the equality given by equation (1) is true only when

n₁ = 1and n₂ = 2.
∴ The transition for n₂ = 2 to n = 1 in hydrogen spectrum would have the same wavelength as Balmer transition n = 4 to n = 2 of He⁺ spectrum.