Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths $r = \frac{\lambda_1}{\lambda_2}$ is given by

As an electron makes a transition from an excited state to the ground state of a hydrogen-like atom/ion:

$A$ hydrogen atom falls from $n^{\text{th}}$ higher energy orbit to the first energy orbit $(n=1)$. The energy released is equal to $12.75 \text{ eV}$. The $n^{\text{th}}$ orbit is:

The ratio of energies of photons produced due to the transition of an electron of a hydrogen atom from its $(i)$ second to first energy level and $(ii)$ highest energy level to $2^{nd}$ level is respectively: (in $: 1$)

An electron collides elastically with an $H$-like atom and excites it from the ground state to $n = 3$. Find the energy transferred to the $H$-like atom in $eV$.

$A$ $12.5 \text{ eV}$ electron beam is used to bombard gaseous hydrogen at ground state. The energy level up to which the hydrogen atoms would be excited is: