What will be the ratio of the wavelength of the third line of the Balmer series in the $He^{+}$ ion spectrum to the first line of the Balmer series in the $Li^{2+}$ ion spectrum?

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 $= 1.6 \times 10^{-19} \, C \, eV^{-1}$)

The value of Rydberg constant $\left(R_H\right)$ is $2.18 \times 10^{-18} \ J$. The velocity of an electron having mass $9.1 \times 10^{-31} \ kg$ in Bohr's first orbit of a hydrogen atom $= \dots \dots \dots \times 10^5 \ ms^{-1}$ (nearest integer).

Photon of the maximum frequency will be absorbed in the transition (for $H$ atom):

Calculate the energy required for the process $He_{(g)}^{+} \rightarrow He_{(g)}^{2+} + e^{-}$. The ionization energy for the $H$ atom in the ground state is $2.18 \times 10^{-18} \, J \, atom^{-1}$.

When electronic transition occurs from a higher energy state to a lower energy state with an energy difference equal to $\Delta E$ electron volts,the wavelength of the emitted line is approximately equal to