**S.A. Goutsmit**and

**G.E. Uhlenbeck**, in 1925, recommended that an electron has an inherent angular momentum that is a magnetic moment which is recognized as

**spin**. In atomic physics, the inherent angular momentum of a particular particle is parametrized by spin quantum number. The spin quantum number is the fourth number. The rest three are a principal quantum number, azimuthal quantum number and magnetic quantum number. The spin quantum number explains the unique quantum state of an electron. This is nominated as ‘s’.

The Spins plays a noteworthy role in quantum mechanics in computing the characteristics of elementary units like electrons. The direction of spin of the particle regulates several things like spin quantum number, angular momentum, the degree of freedom etc. Let us learn more about the electron spin in this segment.

## What is Electron Spin?

The electron spin is one of the three inherent properties of the electrons; the others are mass and charge of the electron. The electron spin is described as the spinning of the electron around its axis.

It is articulated as: \(\left \| S \right \| = \sqrt{s(s+1)h}\)

Where,

**s**is equivalent to a quantized spin vector- The spin vector is articulated as
**||s||** - The spin quantum number
**(s)**is associated with the spin angular momentum and h is the Plancks constant.

**The spin quantum number can be articulated as:** \(S = \frac{n}{2}\)

The permitted values of the spins are 0, 1/2, 1, 3/2, 2, etc.

The intrinsic angular momentum of Electron is signified by quantum number 1/2

**s**is articulated by:

\(S = \sqrt{\frac{3}{4}\bar{h}}\)

Where,

the reduced Planck’s constant is h¯

h¯ = h/2π.

## Electron Spin Theory

The electron spin theory describes the electron as a quantum particle instead of the simple sphere as in the classical theory.

The theory says that the electron spin direction and its influence on the certain properties like magnetic properties of the atom.

### The electron can spin in two directions:

- Spin up
- Spin down

The spin up and spin down direction are corresponding to the spinning in the **+z** or **–z** direction. These spins **(spin up and spin down)** are the particles which have spin **s** equal to 1/2, i.e for electrons.

If the proximate electrons have an opposite spin direction, the magnetic field formed by them cancels each other and no magnetic field is existent.