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The Bohr model of the hydrogen atom (Z = 1) or a hydrogen-like ion (Z > 1), where the negatively charged electron confined to an atomic shell encircles a small, positively charged atomic nucleus and where an electron jumps between orbits, is accompanied by an emitted or absorbed amount of electromagnetic energy (hν). [1]
For an electron to transition between two different states, e.g. ground state to first excited state, it must absorb or emit a photon at an energy matching the difference in the potential energy of those levels, according to the Niels Bohr model, what can be precisely calculated by the Schrödinger equation. Electrons jump between orbitals in a ...
The photon must have higher energy than the sum of the rest mass energies of an electron and positron (2 × 511 keV = 1.022 MeV, resulting in a photon wavelength of 1.2132 pm) for the production to occur. (Thus, pair production does not occur in medical X-ray imaging because these X-rays only contain ~ 150 keV.)
When applied to atomic orbitals, this means that the energy differences between states are also discrete. A transition between these states (i.e., an electron absorbing or emitting a photon) can thus happen only if the photon has an energy corresponding with the exact energy difference between said states. Consider two states of the hydrogen atom:
To escape the atom, the energy of the electron must be increased above its binding energy to the atom. This occurs, for example, with the photoelectric effect, where an incident photon exceeding the atom's ionization energy is absorbed by the electron. [124]: 127–132 The orbital angular momentum of electrons is quantized. Because the electron ...
After the electron has been ejected, the atom is left with a vacant energy level, also known as a core hole. Outer-shell electrons then fall into the inner shell, emitting quantized photons with an energy level equivalent to the energy difference between the higher and lower states. Each element has a unique set of energy levels, and thus the ...
If the electron absorbs a quantity of energy less than the binding energy, it will be transferred to an excited state. After a certain time, the electron in an excited state will "jump" (undergo a transition) to a lower state. In a neutral atom, the system will emit a photon of the difference in energy, since energy is conserved.
This is because, unlike the more common Thomson scattering that happens at the low-energy limit, the energy in the scattered photon in Compton scattering is less than the energy of the incident photon. [6] [7] As the electron is typically weakly bound to the atom, the scattering can be viewed from either the perspective of an electron in a ...