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Table of Allowed Quantum Numbers

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الكلية كلية التربية للعلوم الصرفة     القسم قسم الفيزياء     المرحلة 3
أستاذ المادة فؤاد عطية مجيد       14/12/2016 09:53:24
The energy of the orbitals of a one-electron atom depends only on 1/n2, so the
energy spectrum looks like this, where all orbitals with the same n quantum
number shell are degenerate (i.e. have the same energy).
When describing any element other than Hydrogen, the structure of that atom
will by more complicated than the simple Bohr picture can predict.
1-First, the charge on the nucleus will be larger than +1e. The increased
electrostatic attraction of the electrons to the nucleus will have a
tendency to draw those electrons closer to the nucleus (and as a result
closer to each other). This will lower the total energy of the atom (the
Bohr model can handle this effect)
2- Except for positive ions that contain only a single electron, the electrons
of the atom or ion will interact with each other repulsively, since they
have like charges. This will raise the total energy of the atom and
spread out the electrons. The Bohr model cannot describe electronelectron
repulsion and therefore fails for any multiple electron atom or
ion
The description of how most elemental atoms and ions behave is a balance of
the two above phenomena.
We will treat the way in which the whole atom behaves as the cumulative
behavior of each individual electron. Each individual electron is a wave and
has a wavefunction, which may be described approximately with at orbitals of
Hydrogen. The energy of each of these wavefunctions (orbitals) is qualitatively
different from that of the one-electron atom, however, because of the
discriminatory effects of electron-electron repulsion.


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