The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with maximum wavelength?

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:

$A$ 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 = $-13.6 \ eV$.]

An electron collides with a fixed hydrogen atom in its ground state. The hydrogen atom gets excited and the colliding electron loses all its kinetic energy. Consequently,the hydrogen atom may emit a photon corresponding to the largest wavelength of the Balmer series. The minimum kinetic energy $(K.E.)$ of the colliding electron will be.....$eV$.

An electron of a hydrogen atom in an excited state has an energy $E_n = -0.85 \ eV$. The maximum number of allowed transitions to lower energy levels is:

An electron in a hydrogen atom undergoes a transition from an orbit with quantum number $n_i$ to another with quantum number $n_f$. $V_i$ and $V_f$ are respectively the initial and final potential energies of the electron. If $\frac{V_i}{V_f} = 6.25$,then the smallest possible $n_f$ is: