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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 ...
Each is therefore an unpaired electron, but the total spin is zero and the multiplicity is 2S + 1 = 1 despite the two unpaired electrons. The multiplicity of the second excited state is therefore not equal to the number of its unpaired electrons plus one, and the rule which is usually true for ground states is invalid for this excited state.
The terms 'singlet oxygen' and 'triplet oxygen' derive from each form's number of electron spins. The singlet has only one possible arrangement of electron spins with a total quantum spin of 0, while the triplet has three possible arrangements of electron spins with a total quantum spin of 1, corresponding to three degenerate states.
Singlet state is a molecular electronic state such that all electron spins are paired. That is, the spin of the excited electron is still paired with the ground state electron (a pair of electrons in the same energy level must have opposite spins, per the Pauli exclusion principle).
Examples of atoms in singlet, doublet, and triplet states. In quantum mechanics, a triplet state, or spin triplet, is the quantum state of an object such as an electron, atom, or molecule, having a quantum spin S = 1. It has three allowed values of the spin's projection along a given axis m S = −1, 0, or +1, giving the name "triplet".
The mass of positronium is 1.022 MeV, which is twice the electron mass minus the binding energy of a few eV. The lowest energy orbital state of positronium is 1S, and like with hydrogen, it has a hyperfine structure arising from the relative orientations of the spins of the electron and the positron. The singlet state, 1 S
Furthermore, the spin of each electron previously involved in the bond is conserved, [1] [3] which means that the radical-pair now formed is a singlet (each electron has opposite spin, as in the origin bond). As such, the reverse reaction, i.e. the reforming of a bond, called recombination, readily occurs.
Diradicals are usually triplets.The phrases singlet and triplet are derived from the multiplicity of states of diradicals in electron spin resonance: a singlet diradical has one state (S=0, M s =2*0+1=1, m s =0) and exhibits no signal in EPR and a triplet diradical has 3 states (S=1, M s =2*1+1=3, m s =-1; 0; 1) and shows in EPR 2 peaks (if no hyperfine splitting).