$A$ 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 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?

An electron in a stationary hydrogen atom jumps from the $4^{\text{th}}$ energy level to the ground level. The velocity that the photon acquired as a result of the electron transition will be ($h=$ Planck's constant,$R=$ Rydberg's constant,$m=$ mass of the photon).

Explain emission lines and absorption lines.

The energy levels of a certain atom are $A, B,$ and $C$ in increasing order of energy,i.e.,$E_A < E_B < E_C$. If $\lambda_1, \lambda_2,$ and $\lambda_3$ are the wavelengths of radiation corresponding to transitions from $C$ to $B$,$B$ to $A$,and $C$ to $A$ respectively,which of the following relations is correct?

In an inelastic collision, an electron excites a hydrogen atom from its ground state to an $M$-shell state. $A$ second electron collides instantaneously with the excited hydrogen atom in the $M$-state and ionizes it. At least how much energy must the second electron transfer to the atom in the $M$-state?