Hydrogen-like ions, like He\(^+\), H, and Li\(^+\), all exhibit similar emission spectra because they have only one electron. Their energy levels are governed by the same principles.
The spectrum of He\(^+\) is similar to that of hydrogen (H) because both are hydrogen-like ions. A hydrogen-like ion is any ion with a single electron orbiting the nucleus, so He\(^+\) (which has one electron) behaves similarly to hydrogen (H) in terms of its energy levels and spectral lines. Therefore, their emission spectra follow the same pattern as both follow the Rydberg formula for hydrogen-like ions.