Since ancient times we are wondering what is matter made up of? Democritus said matter is made of indivisible particles and named them Atomos. Maharshi Kanad also named it Anu. Then Dalton came he predicted atoms then J J Thomson gave atomic model by experimenting using cathode rays he said atom is made of negatively charged electrons suspended in positively charged medium and gave analogy of plum pudding or watermelon.
Einstein proved existence of molecules (group of atoms) but still actual model of atom was unknown to the world then great mind Rutherford came and he performed his famous experiment called Rutherford scattering experiment. And he concluded the atom is made of positively charged nucleus and negatively charged electrons revolving around the nucleus in circular orbits like sun-earth system. And showed that maximum space in atom is empty space. But the problem was in circular motion electron has tangential acceleration. From Maxwell's Electromagnetic theory we knew that accelerating charged particle emit electromagnetic radiation. If that's true then electron should emit electromagnetic radiation due to which its energy will decrease which kept it in circular orbit and it will spiral down into nucleus and bammmm... they will neutralize each other which says that atom should not exist at all because of this instability.
So to resolve this idea Neil's Bohr came who is one of the founders of quantum mechanics he said that electrons revolve in some special orbits so that the are not accelerated and don't emit electromagnetic radiation. But if the transition of electron occurs from one orbit or another corresponding amount of energy is released or absorbed depending on transition.
So from previous discussion we knew that light has dual nature particle as well wavy one. After some efforts and experiments we came to know that electrons themselves behave as waves and particles. If they are travelling they show wavy nature if the are interacting they show particle nature. Not just electron but also all the subatomic micro macro particles as well classical bodies show wave nature.
Just the difference is wave nature of particle in subatomic and micro world is much more significant than the classical real macro world because wavelength (distance between crest and trough) of that wave nature depends inversely on mass of object. As the subatomic particles are very small and very light because of this relation its wavelength become more significant as its size. But for heavy bodies because of their huge mass wavelength of associated wave is smaller than atoms themselves so we don't care about it in daily lives. This relation of associated wave nature was give by De-Broglie called as De-Broglie Hypothesis. Experiments were done and wave nature of subatomic particles were confirmed. Famous experiment was Davisson-Germer experiment. Most important thing about this wave is that its not an actual wave but its probabilistic wave. This wave its peaks and valleys which tells how much its likely to find that particle at that position. We will see that later how probabilistic waves determine about its state.
Actual orbit of electron in atom look like this.
But the main conclusion from this discussion was matter also behave as wave so it is called as Matter Waves. It has dual nature wavelike and particle like.
So up till now we know that Waves behave as particles and particles behave as waves so this phenomena called as Dual Nature of Matter and Radiation. If its travelling or in motion and we are not looking at it, it behave as wave but if its interacting and we are looking at that event occurring it will show particle nature.



