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This allowed the orbits of the electron to be ellipses instead of circles, and introduced the concept of quantum degeneracy. The theory would have correctly explained the Zeeman effect, except for the issue of electron spin. Sommerfeld's model was much closer to the modern quantum mechanical picture than Bohr's.
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]
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 ...
Fig. 3: Energies of a photon at 500 keV and an electron after Compton scattering. A photon γ with wavelength λ collides with an electron e in an atom, which is treated as being at rest. The collision causes the electron to recoil, and a new photon γ ′ with wavelength λ ′ emerges at angle θ from the photon's
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:
The electron rescattering model was independently developed by Kuchiev, [47] Schafer et al, [48] Corkum, [49] Becker and Faisal [50] and Faisal and Becker. [51] The principal features of the model can be understood easily from Corkum's version. Corkum's model describes the NS ionization as a process whereby an electron is tunnel ionized.
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 ...
The atom is said to have undergone the process of ionization. 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 ...