YASHPAL KASHYAP

Spin Of A Quarks

 

 

The Elementary Particles , Composite Particles & Atomic Nuclei have a property called Spin”. Spin can be defined as ,

The Angular Momentum Which Is Possessed By Any Of The Sub-Atomic Particles Or Elementary Particles Is Called The Spin” Of That Particle.

The Angular Momentum of a particle are of Two types :

  1. Spin Angular Momentum Or Spin.
  2. Orbital Angular Momentum.

 

In this section of my post, I will be discussing only on the Spin Angular Momentum Or Spin of a particle.

 

One way of thinking of Spin of particles, Is to imagine the particles as little “Tops”, Spinning about an axis. But this could be mis-leading because Quantum Mechanics tells us that the particle do not have any well defined axis.

 

 

Spin Quantum Number :

All the Elementary Particles have some sort of Angular Momentum. That Angular Momentum will have some sort of Magnitude. Same kind of Elementary Particle will have the same Magnitude of Spin Angular Momentum. Thus, As per the Magnitude of  Angular Momentum, Elementary Particles are assigned by the Spin Quantum Number, Which indicate the Magnitude of Angular Momentum of that particular Elementary Particle.

We can calculate the Spin Quantum Number with the formula :

 

s = n / 2

Where,

s is Spin Quantum Number

 n is any Non - Negative Integer

 

We can calculate the Spin Quantum Number of a particle by putting the values in the above equation, For example

 

Let, n = 0

s = n / 2

s = 0 / 2

s = 0

Let, n = 1

s = 1/2

Let, n = 2

s = 1

Let, n = 3

s = 3/2

Let, n = 4

s = 2

And So On.

 

Thus, We get the values of s as, 0, 1/2, 1, 3/2, 2 & so on. We cannot make an Elementary Particle to Spin Faster or Slower. But the Direction of Spin of an Elementary Particle can be changed. The value of s depends only on the type of the Elementary Particle & the value of s cannot be changed.

 

Visualisation Of Spin Of Particles :

 

The Spin of a particle tells us that what a particle looks like from different directions. Let us study some of the examples of how a particle will look from different directions.

Let us consider a particle of Spin 0 or s = 0, So the particle of Spin 0 will look like a “Dot”. As the Dot looks same from every where, The particle of Spin 0 will also look same from every direction.

 

 

Now the particle of Spin 1 or s = 1 will look like an Arrow, As the Arrow look different from every direction, Similarly the particle of Spin 1 will also look different from different direction. Only if one turns round a complete revolution of 360 Degrees, Then the particle looks the same.

 

 

Let us consider a particle of Spin 2 or s = 2, The particle of Spin 2 will look like a Double - Headed Arrow. It also looks different from different directions. But it looks same if one turns it round half a revolution of 180 degrees .

 

Similarly, Higher Spin particles looks the same if one turns them through Small Fractions of one complete revolution. But the extraordinary fact is that, “The particles do not looks the same if one turns them through just One Revolution. Hence, We have to turns them through Two Complete Revolutions. Such Particles are said to have Spin 1/2 or s = 1/2 .

 

 

Categorisation Of Known Particle’s :

 

The particles which are known in the Universe can be divided into two groups:

 

  • The particles which make up the Matter in the Universe are particles of Spin 1/2 or s = 1/2. These particles are also known as “Fermions".
  • The particles which give rise to forces between Matter particles are of Spin 0, 1 & 2 or s= 0, 1 & 2. These particles are also known as  “Bosons”  .

The particles of Spin 1/2 or Fermions”  follows sir “Pauli's Exclusion Principle”.

 

Pauli's Exclusion Principle :

 

Pauli’s Exclusion Principle Says That, Two Similar Particles Or Fermions   Cannot Exist In Same State, i.e. They Cannot Have Both, The Same “ Position”  And Same Velocity”  At Same “Time”, Within The Limits Given By Uncertainty Principle

The Pauli's Exclusion Principle is very important because it explains why Matter Particles do no collapse to form a state of very high density under the influence of the forces produced by the particles of Spin 0, 1, 2 or Bosons. If the particles of Spin 0, 1, 2 or Bosons have same Position as well as same Velocity, Then the particles would all collapse to form a Uniform Dense Matter.

According to the above statement, The particles will nearly have same Positions but they must have different Velocities. They will not stay in same position for long time. Thus, Without Pauli's Exclusion Principle, Quarks would not form separate, Well-Defined Protons & Neutrons .

 

         The Pauli's Exclusion Principle was first discovered in the year of 1925 by Sir “Wolfgang Pauli”. He was honoured with the Nobel Prize for the discovery of the Exclusion Principle, Also known as Pauli's Exclusion Principle”.

 

 

         Thus, Spin of an Elementary Particle is a very important factor, Which also determine the Shape & the Size of Elementary or Matter Particles. Each and every objects around us which we can observe or feel or those objects which are not observable with our naked eyes are composed of Elementary Particles & these Elementary Particles have some sort of Spin. Thus, We can say that the Spin defines our " Building Blocks Of Nature ".