What will be the energy of an electron emitted from the ground state to the $n^{th}$ orbit?

The ratio of the velocity of an electron in the ground state of a hydrogen atom to its velocity in the second excited state of a $He^{+}$ ion is:

Calculate the ionization energy of $H$,$He^{+}$,and $Li^{2+}$ in $kJ \, mol^{-1}$.

The radius of the electron in the first excited state of a hydrogen atom is:

In a hydrogen atom,the energy difference between the states $n = 2$ and $n = 3$ is $E \ eV$. The ionization energy of the $H$-atom is: (in $E$)

The work function for a caesium atom is $1.9 \, eV$. Calculate $(a)$ the threshold wavelength and $(b)$ the threshold frequency of the radiation. If the caesium element is irradiated with a wavelength of $500 \, nm$,calculate the kinetic energy and the velocity of the ejected photoelectron.