# Particle Physics: Why Do Electrons Have Spin of Half?

*Yusrat is a high school student from Bangladesh. She writes about Science & Technology.*

In Physics, Fundamental Particles can be classified as - Particle and Anti particles. An anti particle of a particle shall consist same mass and charge but with opposite sign. When a particle and its anti particle meets, they annihilate and emit energy. But generally a particle and its anti particle never intersects. However particles can be classified as : Fermion and Boson. And the Fermions are called as Quantum Particles.

So what is exactly quantum particle? In Physics, sub-atomic or quantum particles are particles which are pretty much smaller than atoms. Theoretically, 18 quantum particles exist and they are classified as:

a) Quarks

b) Leptons

c) Bosons

One of the surprises of modern physical science is that atoms and sub-atomic particles do not behave like anything we see around us. They are not small toy balls that bounce around; they have wave properties. That's something Newton predicted about light. In fact, according to Wave-Particle Duality property of elements, light and matter exhibit properties of both waves and of particles, which means light and matter have mass (as particle) and certain frequency (like wave) though the frequency of matter depends on its mass, according to De-Broglie’s equation. One of the interesting properties of these particles are Spin. Spin is the total angular momentum, or intrinsic angular momentum, of a body. In fact, the spin of a planet is the sum of the spins and the orbital angular momenta of all its elementary particles. So are the spins of other composite objects such as atoms, atomic nuclei and protons (which are made of quarks). Even these quarks (according to string theory, they are made of strings) have also their own spin!

Spin is built into particles. According to current particle theory, all particles of energy and mass were "born" as the result of various energy fields breaking from one another while the universe expanded and cooled. During this process, every *type* of particle that appeared came with a specific intrinsic angular momentum, or spin. Particles such as electrons and quarks combined to create the first atoms and an additional kind of angular momentum was realized. Electrons orbit nuclei, and in doing so, they exhibit orbital angular momentum in addition to their intrinsic angular momenta. It turns out that neither of these sources of momentum is required to explain why many cosmic objects such as galaxies, stars and solar systems rotate or spin

## All We Know About Electrons

Electrons are tiny compared to protons and neutrons, over 1,800 times smaller than either a proton or a neutron. Electrons have a relative mass of about 9.109x10-31 kg.

J.J. Thomson, a British physicist, discovered the electron in 1897. Originally known as "corpuscles," electrons have a negative charge and are electrically attracted to the positively charged protons. Pathways electrons use to circulate nucleus called orbitals, an idea that was put forth by Erwin Schrödinger, an Austrian physicist, in the 1920s. Today, this model is known as the quantum model or the electron cloud model. The inner orbitals surrounding the atom are spherical but the outer orbitals are much more complicated.

## The Fourth Quantum Number

A Quantum number is a value that is used when describing the energy levels available to atoms and molecules. An electron in an atom or ion has four quantum numbers to describe its state and yield solutions to the Schrödinger wave equation for the hydrogen atom. The four Quantum numbers are -

a) Principal Quantum Number

b) Subsidiary Quantum Number

c) Magnetic Quantum Number

And the very last is d) Spin Quantum Number

These quantum numbers are used to describe the exact whereabouts of an electron in an atom. Spin quantum number is a quantum number that parameterizes the intrinsic angular momentum of an electron.

## But What is Spin?

In quantum mechanics and particle physics, spin is an intrinsic form of angular momentum carried by elementary particles, composite particles, and atomic nuclei. Spin is one of two types of angular momentum in quantum mechanics, the other being orbital angular momentum. But particles like electrons are not spinning at all! Let’s assume electrons are solid spheres. As the electrons have a diameter of near 10 to the negative 18 metres, because of spinning with an angular momentum of one half bar, theoretically the outer edge would be moving at almost 1,00,000 times the speed of light! As the diameter of the electron gets smaller, the faster it would be spinning. So, we can say that no, it’s not spinning. To understand it better, let’s categorize the properties of particles into two group – Intrinsic (according to what they are – mass) and Extrinsic (what they are doing – Velocity). The spin tendency of particles turns out to be in the first group because it’s a type of angular momentum which also get generated because it’s *that *particle! Calling it as intrinsic angular momentum would be way more scientifically accurate.

We know that a charge with certain angular momentum creates its own magnetic field. So do electron, proton, and neutron. And this magnetic field is going to be affected by any other external magnetic field. That is what Stern and Gerlach did in 1912 to detect electron’s spin. In their experiment, they used two strong magnetic poles shaped like this (on fig-1)

For now, consider it as spin separator. As they sent a beam of electrons through it, they found two distinct groups, which can be named as ‘Spin Up (+1/2)’ and ‘Spin Down (-1/2)’ +1/2 and -1/2. In fact, it is true for all other particles including neutrons. *But Neutron has gotten no charge, it is neutral!* Even though it is neutral but smaller particles which it is made of have its own magnetic field. For Spin-1 particles, like neutrons, the charge beam are separated into 3 groups (-1, 0, +1)

## Let's watch this video for better understanding

## Same thing can be explained in an easier way

The Dirac Equation can be significant in understanding the spin of quantum particles. The equation predicted the existence of animatters. It also brought together two of the most important ideas in science: quantum mechanics, which describes the behaviour of tiny objects; and Einstein's special theory of relativity, which describes the behaviour of fast-moving objects. As a result, Dirac's equation describes how particles like electrons behave when they travel close to the speed of light.

Dirac’s wave equation makes use of mathematical objects known as spinors. These can be thought of as the quantum analogue to vectors - a mathematical quantity that has both a value and a direction. Velocity, for example, is a vector composed of speed and direction.

Now Imagine the particle as a little tops spinning about any axis. So according to this concept, the spin of the particle actually tells such what the particle looks like from different direction. A particle of spin 0 is a dot because it looks the same every possible direction. Again, a particle of spin 1 just looks like an arrow. That means it looks different from different direction. If one turns it around a complete revolution (360 degree), the particle will look the same as before. A particle of spin 2 is eventually a like a double-headed arrow. If one turns a half revolution, the particle will look the same. But there are particle which don’t look the same even if you turn one revolution. These particle need to be turned two complete revolution to look the same! One of these particles are electron with Spin of ½!

## Probability

Another way of explaining spin of electron is probability. Probability is the measure of the likelihood that an event will occur. Probability quantifies as a number between 0 and 1. We know Electrons have two type of spin - Spin up and Spin Down. There are also known as clockwise and anticlockwise rotation. From megnetic quantum number we know that Each orbital can accommodate up to two electrons (with opposite spins). That is the maximum number of having electrons in a particular orbital. So the probability of this case will be 1. So now can you calculate what would be the probability of each of electron being situated in the particular orbital? The answer is easy. It is 1÷2= 0.5 or 1/2!

To differentiate each of these sub atomic particles, we use plus (+) and minus (-) as their identity, considering their direction of spin.

## Spin of Protons, MRI and NMR

Stern-Gerlach Experiment for Protons are also similar. If you send beam of protons through the spin separator again, you will find the beam being separated into 4 groups. That’s the prosperity of proton. As the proton is a spin 3/2, these groups are named as +3/2, +1/2, -1/2 and +3/2. (Each quarks has spin of 1/2. As a proton is made three quarks so, the spin of Proton is 3/2)

This property of protons are used in NMR and MRI. Because spin produces Magnetic Field! The human body is mostly water. Water molecules (H2O) contain hydrogen nuclei (protons), which become aligned in a magnetic field. An MRI scanner applies a very strong magnetic field (about 0.2 to 3 teslas, or roughly a thousand times the strength of a typical fridge magnet), which aligns the proton "spins." The scanner also produces a radio frequency current that creates a varying magnetic field. The protons absorb the energy from the magnetic field and flip their spins. When the field is turned off, the protons gradually return to their normal spin, a process called precession. The return process produces a radio signal that can be measured by receivers in the scanner and made into an image

The principle behind NMR is pretty much simple which is: many nuclei have spin and all nuclei are electrically charged. If an external magnetic field is applied, an energy transfer is possible between the base energy to a higher energy level (generally a single energy gap). The energy transfer takes place at a wavelength that corresponds to radio frequencies and when the spin returns to its base level, energy is emitted at the same frequency. The signal that matches this transfer is measured in many ways and processed in order to yield an NMR spectrum for the nucleus concerned.

## A bit about Quarks

In 1964, Gell Mann and George Zweig independently pointed out that eight fold way patterns can be understood in a simpler way if mesons and the barons are built up out of subunits which Gell Mann called Quarks. We generally deal with three or them - Up Quark (Symbol u) Down Quark (Symbol D) and Strange Quark (Symbol S). Collectively they are called Quark Flavours.

Now Each baryon is a combination of three Quarks. With regard to baryon number, we see that any three Quarks (B= +1/3) yield baryon with B= +1. Charges are also work out. The proton has a Quark combination of uud and so its charge quantum number is

q(uud) = 2/3 + 2/3 + (-1/3) = +1

## References

- The spin of a proton – Physics World
- Stern–Gerlach experiment - Wikipedia
- The Weird Quantum Property of 'Spin' | Space
- What exactly is the 'spin' of subatomic particles such as electrons and protons?Does
- Wikipedia

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**© 2018 Yusrat Sadia Nailat**