Electron Orbitals
Electron orbitals are the most probable regions of electrons in atoms and molecules. Electron orbitals can be determined from Schrödinger wave functions. The Schrödinger wave functions of hydrogen atom electrons, in terms of generalized Laguerre polynomials and spherical harmonic functions, are:
where ao = 4πεoħ2 / (mee2) such that εo is the electric constant, ħ is the reduced Planck constant, me is the mass of an electron, and, e is the charge of an electron. E = -mec2α2 / (2n2), L = ħ√l(l + 1) and Lz = ħm where E is the electron energy, L is the electron angular momentum magnitude, Lz is the z component of L, c is the speed of light, and, α = e2 / (4πεoħc).
The electrical potential fields for all electrons in all atoms can be approximated by the electrical potential fields of hydrogen like atoms with suitable effective nuclear charges. Therefore, similar electron orbital approximations can be found for all electrons in all atoms.
Here are plots of various hydrogen electron orbitals:
where ao = 4πεoħ2 / (mee2) such that εo is the electric constant, ħ is the reduced Planck constant, me is the mass of an electron, and, e is the charge of an electron. E = -mec2α2 / (2n2), L = ħ√l(l + 1) and Lz = ħm where E is the electron energy, L is the electron angular momentum magnitude, Lz is the z component of L, c is the speed of light, and, α = e2 / (4πεoħc).
The electrical potential fields for all electrons in all atoms can be approximated by the electrical potential fields of hydrogen like atoms with suitable effective nuclear charges. Therefore, similar electron orbital approximations can be found for all electrons in all atoms.
Here are plots of various hydrogen electron orbitals:
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