In which of the following systems will the radius of the first orbit $(n = 1)$ be minimum?

Consider an electron revolving in a circular orbit of a hydrogen atom,whose quantum number is $n=2$. The velocity of the electron in that orbit is

Consider a hydrogen-like atom whose energy in the $n^{th}$ excited state is given by $E_n = - \frac{13.6 Z^2}{n^2}$. When this excited atom makes a transition from an excited state to the ground state, the most energetic photons have energy $E_{max} = 52.224 \ eV$ and the least energetic photons have energy $E_{min} = 1.224 \ eV$. The atomic number of the atom is:

Would the Bohr formula for the $H-$ atom remain unchanged if the proton had a charge of $+ \frac{4e}{3}$ and the electron a charge of $- \frac{3e}{4}$ (where $e = 1.6 \times 10^{-19} \ C$)? Give reasons for your answer.

The energy of a hydrogen atom in the ground state is $-13.6 \, eV$. The energy of the $He^+$ ion in the first excited state will be .... $eV$.