The energy of an electron in the fourth excited state of the hydrogen atom is

When an electron transition takes place from an excited state to the ground state in a hydrogen atom, then:

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 $\lambda_3$?

$A$ 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

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?

$A$ 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,