The ionization energy of a $Li^{++}$ ion is .......

The time period of revolution of an electron in its ground state orbit in a hydrogen atom is $1.6 \times 10^{-16} \; s$. The frequency of revolution of the electron in its first excited state (in $s^{-1}$) is:

In a hydrogen atom,the electron and proton are bound at a distance of about $0.53 \; \mathring{A}$.
$(a)$ Estimate the potential energy of the system in $eV$,taking the zero of the potential energy at infinite separation of the electron from the proton.
$(b)$ What is the minimum work required to free the electron,given that its kinetic energy in the orbit is half the magnitude of potential energy obtained in $(a)$?
$(c)$ What are the answers to $(a)$ and $(b)$ above if the zero of potential energy is taken at $1.06 \; \mathring{A}$ separation?

The energy level diagram for a hydrogen-like atom is shown in the figure. The radius of its first Bohr orbit is

The energy of $He^{+}$ ion in its first excited state is $......eV$ (The ground state energy for the Hydrogen atom is $-13.6\,eV$).

The ratio of the time periods of the revolution of the electrons in the second and third excited states of a hydrogen atom is