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?

If $n$ is the orbit number of the electron in a hydrogen atom,the correct statement among the following is

Some of the wavelengths observed in the emission spectrum of neutral hydrogen gas are $912, 1026, 1216, 3646, 6563 \, \mathring{A}$. If broadband light is passing through neutral hydrogen gas at room temperature,then the wavelength that will not be absorbed strongly is .................. $\mathring{A}$.

An electron makes a transition from an excited state to the ground state of a hydrogen-like atom. Out of the following statements,which one is correct?

The first excited state of a hydrogen atom is $10.2 \, eV$ above its ground state. The temperature needed to excite hydrogen atoms to the first excited level is

The ratio of the kinetic energies of the electrons in the third and fourth excited states of the hydrogen atom is