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Atomic orbitals are basic building blocks of the atomic orbital model (or electron cloud or wave mechanics model), a modern framework for visualizing submicroscopic behavior of electrons in matter. In this model, the electron cloud of an atom may be seen as being built up (in approximation) in an electron configuration that is a product of ...
The Laporte rule is a selection rule formally stated as follows: In a centrosymmetric environment, transitions between like atomic orbitals such as s-s, p-p, d-d, or f-f, transitions are forbidden. The Laporte rule (law) applies to electric dipole transitions, so the operator has u symmetry (meaning ungerade, odd).
The rules were developed by John C. Slater in an attempt to construct simple analytic expressions for the atomic orbital of any electron in an atom. Specifically, for each electron in an atom, Slater wished to determine shielding constants (s) and "effective" quantum numbers (n*) such that
Potassium and calcium appear in the periodic table before the transition metals, and have electron configurations [Ar] 4s 1 and [Ar] 4s 2 respectively, i.e. the 4s-orbital is filled before the 3d-orbital. This is in line with Madelung's rule, as the 4s-orbital has n + l = 4 (n = 4, l = 0) while the 3d-orbital has n + l = 5 (n = 3, l = 2).
A wave function for a single electron on 5d atomic orbital of a hydrogen atom.The solid body shows the places where the electron's probability density is above a certain value (here 0.02 nm −3): this is calculated from the probability amplitude.
This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The terms atomic orbital and molecular orbital [a] were introduced by Robert S. Mulliken in 1932 to mean one-electron orbital wave functions. [2]
The Born rule [1] [2] [3] provides the means to turn these complex probability amplitudes into actual probabilities. In one common form, it says that the squared modulus of a wave function that depends upon position is the probability density of measuring a particle as being at a given place.
In quantum mechanics, the Pauli exclusion principle (German: Pauli-Ausschlussprinzip) states that two or more identical particles with half-integer spins (i.e. fermions) cannot simultaneously occupy the same quantum state within a system that obeys the laws of quantum mechanics.