One of the simplest yet most profound demonstrations of quantum nature of matter is Young's Double Slit Experiment.
First performed in about 1805 by English scientist Thomas Young it proved that light had wave properties in that two coherent sources of light could interact with each other to create an interference pattern in a way similar to how water waves interact with each other.
Young used sunlight shining through a pinhole to create a coherent light source. This light was shone onto a barrier penetrated by two narrow slits separated by a distance 'd' from each other. Located a much futher distance 'D' away from the two slits was a screen onto which was illuminated by the dual slit light source.
The result as Young demonstrated was a modulated pattern of bright and dark regions. Bright regions appeared where the light waves were in phase and hence added together to create areas of maximum intensity. Dark regions occurred where the light waves were out of phase and cancelled one another out to leave regions with no light energy.
Assuming that 'D' is very much larger than 'd' light travelling from slit #2 to the screen will go a distance farther than light travelling fron slit #1 to the screen. If the difference in the length of the two paths is an integer multiple of the wave length of light then the light interferes constructively causing a bright spot.
This simple experiment demonstrated that light had wave like properties and that it had a wavelength associated with it that could be measured using the geometry of the double slit experiment. As you will see later the Compton Effect demonstrates that light also emodies the charateristics of a stream of particles, thus the wave particle duality which we discussed at the out set.
Much later, the double slit experiment was performed on an electron stream and it was demonstrated the electrons have a characteristic wave length equal to h/mv where 'h' is Planck's constant and 'mv' is the electon's momentum calculated as mass times velocity.