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A pair of electrons in a spin singlet state has S = 0, and a pair in the triplet state has S = 1, with m S = −1, 0, or +1. Nuclear-spin quantum numbers are conventionally written I for spin, and m I or M I for the z-axis component.
For example, if two electrons reside in the same orbital, then their values of n, ℓ, and m ℓ are equal. In that case, the two values of m s (spin) pair must be different. Since the only two possible values for the spin projection m s are +1/2 and −1/2, it follows that one electron must have m s = +1/2 and one m s = −1/2.
The electrons in non-coincident pairs are shown using thin lines and the coincident electron pairs are shown using thick lines. (b) The ELF for the ClF 3 molecule generated using an η=0.700 value for the isosurfaces.
In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1/2 massive particles, called "Dirac particles", such as electrons and quarks for which parity is a symmetry.
The ability of positronium to form both singlet and triplet states is described mathematically by saying that the product of two doublet representations (meaning the electron and positron, which are both spin-1/2 doublets) can be decomposed into the sum of an adjoint representation (the triplet or spin 1 state) and a trivial representation (the ...
When a proton encounters its antiparticle (and more generally, if any species of baryon encounters the corresponding antibaryon), the reaction is not as simple as electron–positron annihilation. Unlike an electron, a proton is a composite particle consisting of three "valence quarks" and an indeterminate number of "sea quarks" bound by gluons.
The wave function of fermions, including electrons, is antisymmetric, meaning that it changes sign when two electrons are swapped; that is, ψ(r 1, r 2) = −ψ(r 2, r 1), where the variables r 1 and r 2 correspond to the first and second electrons, respectively. Since the absolute value is not changed by a sign swap, this corresponds to equal ...
In chemistry, an electron pair or Lewis pair consists of two electrons that occupy the same molecular orbital but have opposite spins. Gilbert N. Lewis introduced the concepts of both the electron pair and the covalent bond in a landmark paper he published in 1916. [1] [2]