Which of the following relations is applicable for any $H$-like species?

The ionization energy of $He^+$ is $19.6 \times 10^{-18} \ J \ atom^{-1}$. What is the energy of the first stationary state $(n = 1)$ of $Li^{2+}$?

If $\lambda_0$ and $\lambda$ are the threshold wavelength and the wavelength of incident light,respectively,the velocity of the photoelectron ejected from the metal surface is:

The ratio of the slopes of the $KE_{max}$ vs $v$ and $V_0$ vs $v$ curves in the photoelectric effect gives ($v$ is the frequency of incident radiation and $V_0$ is the stopping potential).

Calculate the ratio of the radius of the $2^{nd}$ and $3^{rd}$ orbit of a hydrogen atom. (Note: $r_n \propto n^2$)

What is the work function of the metal if the light of wavelength $4000 \, \mathring{A}$ generates photoelectrons of velocity $6 \times 10^5 \, ms^{-1}$ from it? ............. $eV$ (Mass of electron $= 9 \times 10^{-31} \, kg$; Velocity of light $= 3 \times 10^8 \, ms^{-1}$; Planck's constant $= 6.626 \times 10^{-34} \, Js$; Charge of electron $= 1.6 \times 10^{-19} \, C \, eV^{-1}$)