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 $eV$.

Transitions between three energy levels in a particular atom give rise to three spectral lines of wavelengths $\lambda_1, \lambda_2$ and $\lambda_3$. Given that the wavelengths are in increasing order of magnitude,which one of the following equations correctly relates $\lambda_1, \lambda_2$ and $\lambda_3$?

The ground state energy of a hydrogen atom is $-13.6 \, eV$. When its electron is in the first excited state,its excitation energy is ...... $eV$.

$A$ photon of wavelength $\lambda$ is absorbed by an electron confined to a box of length $L = \sqrt{(35 h \lambda / 8 m c)}$. As a result,the electron makes a transition from state $k=1$ to the state $n$. Subsequently,the electron transitions from the state $n$ to the state $m$ by emitting a photon of wavelength $\lambda^{\prime} = 1.75 \lambda$. Then,

In a sample of hydrogen-like atoms,all of which are in the ground state,a photon beam containing photons of various energies is passed. In the absorption spectrum,five dark lines are observed. The number of bright lines in the emission spectrum will be (assume that all transitions take place).

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.