What would you say if someone asks you about an electron’s spin? Well, the first line of our answer would be, “an electron is a spin half particle.” Isn’t it? Not only the electron but all the fermions also have a half-integral spin while all the bosons possess an integral spin. But what does this spin actually represent? Are these subatomic particles actually spinning around their axis, and their spin is actually a measure of how much they spin? Or does the concept of spin has something completely different to offer? Well, these questions have been embedded in our minds for a long time, but we are not yet very clear of what this term “spin” actually represents.

## Do electrons spin around their axis?

Our Earth spins around its axis, but it would be a mistake to view electrons as little billiard balls spinning in space like a planet. Although electrons have a property called spin, it’s a lot fuzzier than what it spells to be. An electron is a spin half particle, giving out its spin angular momentum (1/2)ħ (we will discuss this later). If this quantity is true, then considering the electron’s mass and size, it should spin with a rotational velocity equivalent to the speed of light, which is not practical. So the only conclusion is that an electron can’t spin about its own axis, and thus, spin is just a representative term.

## So what does an electron’s spin actually stands for?

Each particle in our universe has some intrinsic properties and some extrinsic properties. Intrinsic properties are the inherent properties of a particle, while extrinsic properties are acquired depending upon external factors. For example, our blood group is our intrinsic property, while our behavior is an extrinsic one. An electron has three main intrinsic properties, and the spin is one of them, with the other two being mass and charge.

An electron’s spin is related to the electron’s inherent angular momentum, i.e., the spin angular momentum. The spin multiplied by ħ (the reduced Planck’s constant) gives the value of the electron’s intrinsic spin angular momentum. It is independent of all other properties of the electron, even its orbital angular momentum. So, spin is just the angular momentum that a particle has just because it’s that particle!

## The discovery of electron’s spin

In 1920, Otto Stern and Walter Gerlach designed an experiment, which unintentionally led to discovering an electron’s spin. In the revolutionary “Stern Gerlach experiment,” Otto Stern and Walter Gerlach put a bunch of silver atoms in an oven and vaporized them. These silver atoms’ beam was then passed through a magnetic field where it split into two beams.

To explain these observations, it was stated that an electron has a magnetic field due to its intrinsic spin. Whenever the electrons having opposite spins are put together, there is no net magnetic field. However, the silver atom used in the experiment had 47 electrons, 23 of one spin type and 24 of the opposite type. The electron pairs of the opposite spins canceled each other out, but one unpaired electron was left that gave the atom its spin, thereby leading the atoms to behave in an observed manner.

Since there was a high likelihood for either spin to exist due to many electrons in the beam of atoms, so when the atoms went through the magnetic field, they got split into two beams. And these two orientations of spin were termed +1/2 and -1/2.

Moreover, In 1925, Samuel Goudsmit and George Uhlenbeck claimed that some of the mischievous features of the hydrogen spectrum could be successfully explained by assuming that electrons act as if they actually have a spin.

## Electron’s spin vs its spin quantum number

We often treat the electron’s spin and the electron spin quantum number as the same thing. Although both these entities are very closely related, they are not the same. While the electron’s spin is denoted by s, the spin quantum number is denoted by ms. The spin has only one value, like 1/2 in the case of electrons. However, the spin quantum number ms represent the spin’s possible orientations, such as -1/2 or +1/2, or spin down or spin up configuration.

The concept of spin undoubtedly plays a noteworthy role in quantum mechanics. It contributes to computing the characteristics of elementary particles like electrons and even regulates large atoms’ behavior on the whole. I have tried to keep this article as simple as possible without delving into the complex mathematics involved to make the basics clear. Maybe we can discuss the complex formulations related to spin in future articles.
Till then, Happy learning!

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