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Spin is described mathematically as a vector for some particles such as photons, and as a spinor or bispinor for other particles such as electrons. Spinors and bispinors behave similarly to vectors: they have definite magnitudes and change under rotations; however, they use an unconventional "direction". All elementary particles of a given kind ...
Because electrons are fermions, the Pauli exclusion principle forbids these particles from having all the same quantum numbers. Therefore, for two electrons to occupy the same orbital, and thereby have the same orbital quantum number, they must have different spin quantum numbers. This also limits the number of electrons in the same orbital to two.
Within a molecule, electrons move under the influence of several nuclei, and occupy molecular orbitals; much as they can occupy atomic orbitals in isolated atoms. [128] A fundamental factor in these molecular structures is the existence of electron pairs. These are electrons with opposed spins, allowing them to occupy the same molecular orbital ...
Spin quantum numbers apply also to systems of coupled spins, such as atoms that may contain more than one electron. Capitalized symbols are used: S for the total electronic spin, and m S or M S for the z-axis component. 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.
Spin states relate to chemical and biochemical reaction mechanisms because bonds can be formed only between two electrons of opposite spin (Hund's rules). Sometimes when a bond is broken in a particular manner, for example, when struck by photons, each electron in the bond relocates to each respective molecule, and a radical-pair is formed.
Each has two electrons of opposite spin in the π* level so that S = 0 and the multiplicity is 2S + 1 = 1 in consequence. In the first excited state, the two π* electrons are paired in the same orbital, so that there are no unpaired electrons. In the second excited state, however, the two π* electrons occupy different orbitals with opposite spin.
Quantum entanglement is the phenomenon of a group of particles being generated, interacting, or sharing spatial proximity in a manner such that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance.
By contrast, strongly interacting particles like slow electrons and molecules require vacuum: the matter wave properties rapidly fade when they are exposed to even low pressures of gas. [67] With special apparatus, high velocity electrons can be used to study liquids and gases. Neutrons, an important exception, interact primarily by collisions ...