Find the ratio of energies of photons produced due to the transition of an electron in a hydrogen atom from its $(i)$ second permitted energy level to the first level,and $(ii)$ the highest permitted energy level to the first permitted level.

If energy of $15 \ eV$ is given to an electron in the $4^{th}$ orbit,find its final energy when it comes out of the $H$-atom. (in $eV$)

The energy of an electron in the $n^{th}$ orbit of a hydrogen atom is given by $E_n = -\frac{13.6}{n^2} \, eV$. How much energy in $eV$ is required to move an electron from the $n = 2$ orbit to the $n = 3$ orbit?

$A$ hydrogen atom at the ground level absorbs a photon and is excited to $n=4$ level. The potential energy of the electron in the excited state is

When a hydrogen atom emits a photon during a transition from $n=4$ to $n=2$,its recoil speed is about (in $m \ s^{-1}$)

The total energy of an electron in the first excited state of the hydrogen atom is about $-3.4 \; eV.$
$(a)$ What is the kinetic energy of the electron in this state?
$(b)$ What is the potential energy of the electron in this state?
$(c)$ Which of the answers above would change if the choice of the zero of potential energy is changed?