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The important feature of the spinning electron is the spin angular momentum vector, which we label \(S\) by analogy with the orbital angular momentum \(L\).
Spin angular momentum of electron. Electrons have intrinsic angular momentum characterized by quantum number 1/2. The magnetic moment of an electron is approximately twice what it should be in classical mechanics. S = 1/2 specifically for electrons.
An electron spin s = 1/2 is an intrinsic property of electrons. G s ≈ 2 {\displaystyle g_{\rm {s}}\approx 2}. The spin g -factor is approximately two:.
Bohr’s atomic model laid down various postulates for the arrangement of electrons in different orbits around the nucleus. In a way analogous to other quantized angular momenta, L, it is possible to obtain an expression for the total spin angular momentum:. S = ℏ 1 2 ( 1 2 + 1 ) = 3 2 ℏ.
Since J = L + S, in the weak magnetic field case, (I'm imagining the vector model of the atom) if L is really large, could electrons have very large total angular momentum J?. The spin angular momentum is characterized by a quantum number;. Nonetheless it is angular momentum and any angular momentum associated with a charged particle results in a magnetic dipole moment, which is the source of a magnetic field.
The electron spin angular momentum is a fundamentally different property that is intrinsic to the particle and therefore does not depend on the motion of the electron. We define spin angular momentum operators with the same properties that we found for the rotational and orbital angular momentum operators. Spin is one of two types of angular momentum in quantum mechanics, the other being orbital angular momentum.
In the pattern of other quantized angular momenta, this gives total angular momentum The resulting fine structure which is observed corresponds to two possibilities for the z-component of the angular momentum. The orbital angular momentum operator is the quantum-mechanical counterpart to the classical angular momentum of orbital revolution and appears when there is periodic structure to its wavefunction as the angle varies.
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