In a hydrogen atom,which of the following transitions will have the minimum wavelength?

In an atom,an electron requires $47.2 \, eV$ of energy to transition from the $n = 2$ orbit to the $n = 3$ orbit. The atomic number $Z$ of the atom is:

The energy of the highest energy photon of the Balmer series of the hydrogen spectrum is close to $... eV$.

The diagram below shows the lowest four energy levels for an electron in a hypothetical atom. The electron is excited to the $-1\,eV$ level and transitions to the lowest energy state $(-12\,eV)$ by emitting exactly two photons. Which of the following energies could not belong to either of the photons (in $eV$)?

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?

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