Electron Spin

Electron spin refers to a quantum property of electrons and it also is a form of angular momentum. Furthermore, the magnitude of this angular momentum happens to be permanent. Also, the electron spin is a fundamental property just like charge and rest mass.

Introduction to Electron Spin

S.A. Goutsmit and G.E. Uhlenbeck, in 1925, came up with the idea that an electron has an inherent angular momentum that can be recognized as a spin. Furthermore, in atomic physics, any particle’s inherent angular momentum is parametrized by spin quantum numbers. Also, the spin quantum number is the fourth number while the rest three are a magnetic quantum number, principal quantum number, and azimuthal quantum number.

The spin quantum number gives us an explanation of an electron’s unique quantum state. Moreover, the nomination of this takes place as ‘s’. Also, the spins play a significantly important role in quantum mechanics in order to compute the characteristics of elementary units like electrons.

electron spin

                                                                                                                     Electron Spin

Theory of Electron Spin

The electron spin theory describes the electron as a quantum particle rather than a simple sphere as in the classical theory. Furthermore, the theory tells us about the direction of the electron spin. Moreover, it also discusses its influence on certain properties like the atom’s magnetic properties.

Electron Spin Directions

There are two main electron spin directions: spin up and spin down. Furthermore, the spin up and spin down direction correspond to the spinning in the +z or –z direction. Moreover, these spins (spin up and spin down) refer to the particles whose spin is equal to 1/2, i.e. for electrons.

In quantum theory, an electron can be considered like a minute magnetic bar. Furthermore, one can consider spin points of an electron like the north pole of the minute bar. If two proximate electrons are characterized by similar spin direction, the formation of the magnetic field by them strengthens each other.

Consequently, the gaining of a strong magnetic field takes place. If the proximate electrons have an opposite spin direction, the magnetic field that results from them would cancel each other. As such, no magnetic field would be existent.

Formula of Electron Spin

The electron spin happens to be one of the three inherent properties of the electrons. Furthermore, the other properties are an electron’s mass and charge. Moreover, the electron spin can be simply referred to as an electron’s spinning around its axis.

Its representation can take place as: \(\left \|S \right \| = \sqrt{s\left ( s + 1 \right )h}\)


s is equivalent to a spin vector that is quantized

The spin vector is articulated as ||s||

The association of the spin quantum number (s) is with the spin angular momentum and h represents the Plancks constant.

One can articulate the spin quantum number as: S = n/2

Any non-negative integer can be n.

As far as the electron spin value is concerned, the permitted values are 0, 1/2, 1, 3/2, 2, etc.

The intrinsic angular momentum of Electron can be represented by quantum number 1/2

The total angular momentum s is articulated by:

s = \(\sqrt{n\left ( n + 1 \right )h}\)

s = \(\sqrt{\frac{1}{2}\left ( \frac{1}{2} + 1 \right )h}\)

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


h¯ represents the reduced Planck’s constant

h¯ = h/2π.

FAQs For Electron Spin

Question 1: What is spin or electron spin?

Answer 1: An electron spin refers to a form of angular momentum of electrons. Furthermore, it is a quantum property of electrons and its magnitude happens to be permanent.

The spin quantum number provides information about an electron’s unique quantum state. Also, the spins play an important role in quantum mechanics. This facilitates the computation of the characteristics of elementary units like electrons.

Question 2: How can one identify an electron spin?

Answer 2: One can identify an electron spin by following the three steps:

  • Determining the number of electrons an atom contains.
  • Drawing an atom’s electron configuration. One can take a look at the electronic configurations to gain more information for this purpose.
  • Distributing the electrons by using up and down arrows so as to show the electron spin direction.
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