Which of the following phenomena suggests the presence of electron energy levels in atoms?

Total energy of an electron in an excited state of a hydrogen atom is $-3.4 \text{ eV}$. Find the kinetic and potential energy of the electron in this state.

Due to transitions among its first three energy levels,a hydrogenic atom emits radiation at three discrete wavelengths $\lambda_1, \lambda_2$ and $\lambda_3$ (where $\lambda_1 < \lambda_2 < \lambda_3$). Then,

The diagram shows different transitions across the energy levels for an electron in a certain atom. Among these,which transition represents the emission of a photon with the most energy?

$A$ hydrogen atom makes a transition from $n = 2$ to $n = 1$ and emits a photon. This photon strikes a doubly ionized lithium atom $(Z = 3)$ in an excited state and completely removes the orbiting electron. The least quantum number for the excited state of the ion for this process is:

What is the ratio of the total energy of an electron in a hydrogen atom in the first excited state to that in the third excited state?