Explain why a 5eV photon of light cannot be absorbed or emitted by the hydrogen atom

None of the transitions in the hydrogen atom corresponds to a photon energy of 5eV hence no photon of this energy is absorbed or emitted by the hydrogen atom.

Explanation:

Electrons in a hydrogen atom must be in one of the allowed energy levels. If an electron is in the first energy level, it must have exactly -13.6 eV of energy. If it is in the second energy level, it must have -3.4 eV of energy and so on.

If the electron wants to jump from the first energy level, n = 1, to the second energy level n = 2. The second energy level has higher energy than the first, so to move from n = 1 to n = 2, the electron needs to gain energy. It needs to gain (-3.4) - (-13.6) = 10.2 eV of energy to be excited to the second energy level.

The step from the second energy level to the third is much smaller. It takes only 1.89 eV of energy for this excitation to take place. It takes even less energy to excite electrons in hydrogen from the third energy level to the fourth, and even less from the fourth to the fifth.

None of these transitions in the hydrogen atom corresponds to a photon energy of 5eV hence no photon of this energy is absorbed or emitted by the hydrogen atom.