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In 1940, Pauli proved the spin–statistics theorem, which states that fermions have half-integer spin, and bosons have integer spin. [7] In retrospect, the first direct experimental evidence of the electron spin was the Stern–Gerlach experiment of 1922. However, the correct explanation of this experiment was only given in 1927. [38]
When atoms have even numbers of electrons the spin of each electron in each orbital has opposing orientation to that of its immediate neighbor(s). However, many atoms have an odd number of electrons or an arrangement of electrons in which there is an unequal number of "spin-up" and "spin-down" orientations.
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.
Electrons in metals also behave as if they were free. In reality the particles that are commonly termed electrons in metals and other solids are quasi-electrons—quasiparticles, which have the same electrical charge, spin, and magnetic moment as real electrons but might have a different mass. [134]
In the case of electrons in atoms, the exclusion principle can be stated as follows: in a poly-electron atom it is impossible for any two electrons to have the same two values of all four of their quantum numbers, which are: n, the principal quantum number; ℓ, the azimuthal quantum number; m ℓ, the magnetic quantum number; and m s, the spin ...
The Pauli exclusion principle states that no two electrons in an atom can have the same values of all four quantum numbers. If there are two electrons in an orbital with given values for three quantum numbers, (n, ℓ, m), these two electrons must differ in their spin projection m s.
Note that μ is a negative constant multiplied by the spin, so the magnetic moment is antiparallel to the spin angular momentum. The spin g-factor g s = 2 comes from the Dirac equation, a fundamental equation connecting the electron's spin with its electromagnetic properties. Reduction of the Dirac equation for an electron in a magnetic field ...
Spin- 1 / 2 particles can have a permanent magnetic moment along the direction of their spin, and this magnetic moment gives rise to electromagnetic interactions that depend on the spin. One such effect that was important in the discovery of spin is the Zeeman effect , the splitting of a spectral line into several components in the ...