JEE Advanced 2023 Physics question on Atoms and Nuclei

A Hydrogen-like atom has atomic number $Z$. Photons emitted in the electronic transitions from level $n = 4$ to level $n = 3$ in these atoms are used to perform photoelectric effect experiment on a target metal. The maximum kinetic energy of the photoelectrons generated is $1.95$ eV. If the photoelectric threshold wavelength for the target metal is $310$ nm, the value of $Z$ is _______.

[Given: $hc = 1240$ eV-nm and $Rhc = 13.6$ eV, where $R$ is the Rydberg constant, $h$ is the Planck's constant and $c$ is the speed of light in vacuum]