Mathematical proofs of charge on Sub-Atomic Particle

Mathematical proofs of charge on Sub-Atomic Particle

Today we will explore the intresting mathematical proofs of charge on Sub-Atomic particles. 

So, here we go . 👇👇👇

So, as we know that the atom has its three fundamental sub-atomic particles i.e. Protons, Neutrons and Electrons. 

These particles have their own particular charge.

1) . Proton :- positive charge (+1).

2) . Neutron :- neutral charge (0) .

3) . Electron :- negative charge (-1).

The atom has nucleus , in which proton and neutron stay together. And basically, it's overall mass is concentrated in nucleus. 

It also have energy shells in which Electron used to revolve nucleus. Each shell has its particular energy limits. 

Now, before proving " how to prove the charge of subatomic particles mathematically?". We should know more about proton , neutron and Electron.

So, protons are positively charged particles in atoms. They are the member of Hadrons group. That means, they are also made up of more simpler particles - QUARKS .
As the quarks are of six types :-
1) .Up quark
2). Down quark
3). Strange quark
4). Charm quark
5) .top quark
6). Bottom quark

Up quark, charm quark and top quark has the charge of 2/3.

Down quark, strange quark and bottom quark has the charge of -1/3.

So, the protons are also made up of two up quark and one down quark.

In same way, Neutrons are also the member of Hadron group. But these have neutral charge or no charge. So, neutron are also made up of quarks. It has two down quarks and one up quark.

Whereas, Electrons belong to leptons group . That means they are not quark based particles.

Now , let's know how to prove the charge of sub atomic particles mathematically.

How to prove charge of proton mathematically? 

We know that, protons are made up of quarks. They have two up quarks and one down quark.

So,
Charge of up quark = 2/3
Charge of down quark = -1/3

Finally,

Charge of Proton = 2(charge of up quark) + charge of down quark.

Charge of proton = 2(2/3)+-1/3
                                = 4/3-1/3
                                = 3/3
                                = 1

Hence, Proton has the charge of positive one (+1).

How to prove the charge of neutron mathematically?

We know that neutrons are made up of two down quarks and one up quark.

So,
Charge of up quark = 2/3
Charge of down quark = -1/3

Finally,

Charge of neutron = 2(charge of down quark) + charge of up quark.

Charge of neutron = 2(-1/3)+2/3
                                  = -2/3+2/3
                                  = 0

Hence, the Neutrons have neutral charge or zero charge.

How to prove the charge of Electron mathematically?

To prove this , let's have a look on the charge of whole atom.
What's its charge?
Obviously , the atom is electrically neutral.
And
We also know that the Electron is lepton that means, its not quark based particle.

So, we can't prove its charge in previous way.
But
Its easier than our previous efforts.
Let the charge of Electron be x.

By above statements,
Charge of atom = charge of proton+ charge of neutron+ charge of Electron.

0= 1+0+x
0=1+x
x=-1

Hence, the charge of Electrons are negative one (-1).

Hope u enjoyed it.
I will be back with more interesting topics .