This is a great new world and quantum mechanics made it magical as objects become wave and light become particle. From the perspective of an ordinary man who doesn't have to do anything with physics,it may sound crazy but it is the truth. Although it all started with just a theory or assumption.

During the beginning of 20^th century, Planck was trying to explain blackbody radiation and it couldn't be explained without assuming that light comes in discrete packets of energy and we call it photon. Planck didn't truly believe in his theory and he used a constant as well, named after his name, Planck constant. Einstein came to the same conclusion but this time the issue was different. It was photoelectric effect. But they came to the same conclusion that light comes as a discrete packets of energy.

Source :Wikicommons CCO

Photon of frequency can have energy

here h is Planck's constaant.
If you think light is particle like the normal sense then you are mistake, the same with matter as wave. Its mostly metaphor. It is most the language of physics rather than in the normal sense.

We can literally create electromagnetic wave in the microscopic world just by waving a charge back and forth. This will create a disturbance which will propagate through the space in a finite speed and acts like a free radiation. If we solve the Maxwell equation with proper initial condition we can easily find the nature of electromagnetic field all around.

When a particle radiates, it emits a photon and it can also absorb photon but only one at a time. To describe this process of transition, we use transition rates. Now what is transition rate? It is the squared modulus of transition amplitude. This is what all matters and we measure it experimentally and calculate it in theory. Now lets analyze some property of photon.

Properties of Photon

The most important property of photon is that it is massless particle with spin 1. It travels with the speed of light in vacuum and at a momentum p =E/c. Spin can be parallel or anti-parallel to the momentum which depend on its polarization. If it is left circularly polarized or right. The momentum and polarization are described by quantum numbers and this quantum numbers describe the state of the particle

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Lets think that we stimulated one mole of hydrogen gas to emit light. So, what will happen? Well in one mole there are Avogadro number of hydrogen atom and as every atom will emit a photon. This photons will create a dense gas of photon which can be described by classical electromagnetism.

Although photons are emitted one at a time but successively create photons are related. We can see that when photons go through two slits one after another it can create a diffraction pattern behind the slit on the detention screen.

Wave Particle Duality

Wikicommons CCO

There is a history of debate what light is? Is it a particle or is it a wave? Well quantum physics says its both. But lets not be mistaken by our normal perception about wave a particle. As I said above, its a metaphor. It comes into play when you can specifically tell that something is in a specific place. Well, if you can tell that that's a particle if you cant, then you say its wave. That is another topics for another day, we will talk about it later.

So, now what what is wave particle duality? It is light is wave a particle at the same time . I will solve some general equation but don't be worried. Its the most simple mathematics I think which De Broglie won a Nobel prize for.

Here we can see in the same equation there is and p together. depict the wavelenth which is the characteristics of wave and P is momentum which describes the characteristics of particle. So, this equation shows the wave and particle duality.
Enough of mathematics, lets think from the perspective of our normal life. Think of two classmates of yours are in love with each other. So, If I ask about the girl's position, you say that she is with her lover. In this way you fix her position and she becomes a particle. Next day think they broke up. Now I ask again where she is. You say somewhere in the campus. She can be anywhere inside the campus. Her position is not fixed. So, now she is a wave. You can she now the same thing can be wave as well as particle. That's all for today. I appreciate your comments.

References

<1>Kerson Huang, Fundamental forces of nature

<2>Wiki

<3>David griffith, Introduction to quantum mechanics