The energy levels for an electron in a certain atom are shown in the figure. Which of the following transitions will emit a photon with the highest energy?

With the increase in principal quantum number,the energy difference between two successive energy levels

$A$ 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,

$A$ sample of hydrogen atoms is in an excited state (all the atoms). The photons emitted from this sample are made to pass through a filter through which light having a wavelength greater than $800 \ nm$ can only pass. Only one type of photon is found to pass through the filter. The sample's initial excited state is: [Take $hc = 1240 \ eV \cdot nm$,ground state energy of hydrogen atom = $-13.6 \ eV$.]

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

The ratio of energies of photons produced due to transition of an electron in a hydrogen atom from the second energy level to the first energy level and from the fifth energy level to the second energy level is: