What is the energy of a photon that, when absorbed by a...

What is the energy of a photon that, when absorbed by a hydrogen atom, could cause an electronic transition from (a) the $n=2$ state to the $n=5$ state and (b) the $n=4$ state to
the $n=6$ state?

Key Concepts

Bohr Model

The Bohr model provides a framework for understanding the behavior of electrons in a hydrogen atom by postulating that electrons move in discrete orbits with quantized energy values. It explains why only specific photon energies, corresponding to the energy differences between these orbits, can be absorbed or emitted, thus leading to the characteristic spectral lines observed in hydrogen.

Hydrogen Atom Energy Quantization

In a hydrogen atom, electrons occupy discrete energy levels that are determined by quantum mechanics. The energy associated with each level can be expressed using the formula E_n = -13.6 eV/n^2, where n is the principal quantum number. This quantization is a key concept in atomic physics and underpins the absorption and emission of light by the atom.

Photon Energy

Photon energy is determined by the difference in energy levels between the initial and final states of an atom. It is given by the equation E = E_final - E_initial, which reflects how a photon must have an energy that exactly matches the gap between these quantized states in order to be absorbed or emitted.

Electronic Transitions

Electronic transitions refer to the process where an electron in an atom absorbs or emits energy and moves between different quantized energy levels. These transitions are fundamental for understanding atomic spectra and are directly related to the absorption or emission lines observed in the atomic spectrum.

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