If the shortest wavelength of H atom in Lyman series is ‘x’ , then longest wavelength in Balmer series of  He⁺ is

The problem asks for the longest wavelength in the Balmer series of the He⁺ ion, given that the shortest wavelength in the Lyman series of the hydrogen atom is 'x'. Let's break this down step-by-step.

The shortest wavelength in the Lyman series corresponds to the transition from $n = 2$ to $n = 1$ in the hydrogen atom. Using the Rydberg formula, the wavelength for any transition in the Lyman series of H is given by: