Electron Spin - Physics

In 1925, Samuel Goutsmit and G.E. Uhlenbeck proposed that an electron possesses an inherent angular momentum in the form of a magnetic moment known as a spin. A particle's inherent angular momentum is parametrized by its spin quantum number in atomic physics. The number four is the spin quantum number. A primary quantum number, an Azimuthal quantum number, and a magnetic quantum number make up the remaining three. An electron's unique quantum state is explained by its spin quantum number. The letter ‘s' is used to represent this.
In quantum mechanics, spins play a significant role in computing the properties of fundamental units such as electrons.

The spin quantum number, angular momentum, degree of freedom, and other properties of a particle are all governed by its spin direction. In this segment, we'll learn more about electron spin.

What is the meaning of electron spin?

The electron spin is one of three intrinsic properties of electrons, the other two being the mass and the charge. The spinning of an electron around its axis is referred to as the electron spin.
It is viewed as follows -

‖S‖= √s (s+1) h

Where,
A quantized spin vector is equivalent to s.
The spin vector is denoted by the symbol ||s||.
The spin angular momentum is connected with the spin quantum number (s), and Planck’s constant is h.

The formula for the spin quantum number is -
S = n / 2

n can be any non-negative integer.
The spins can have values of 0, 1/2, 1, 3/2, 2, and so on.
Quantum number 1/2 represents the intrinsic angular momentum of the electron.
The total angular momentum s is defined as follows:

s = √ n (n+1) h
s = √ 1 / 2 (½+1) h
s = √ 3 / 4 h

Theory of Electron Spin

In contrast to the classical theory, which depicts the electron as a simple sphere, the electron spin theory depicts it as a quantum particle.

According to the above-mentioned theory, the electron spin direction has an impact on certain properties of the atom, such as its magnetic properties.

The electron can spin in two directions namely clockwise and counter-clockwise. It is also summarised as upwards and downwards
The spinning in the +z and –z directions correspond to the spin up and spin down directions. The particles with spin s, equal to 1/2, i.e., electrons, have these spins, namely spin up and spin down. Each type is given a magnitude of +1/2 and -1/2 respectively.

The electron is modeled after a minute magnetic bar in quantum theory, with its spin pointing to the minute bar's north pole. The magnetic field created by two adjacent electrons with comparable spin directions enhances each other, resulting in a strong magnetic field. If the spin directions of the proximate electrons are opposite, the magnetic field induced by them cancels out, and no magnetic field is produced.