This can be explained on the basis of dual nature of matter...
WAVE AND PARTICLE DUALITY OF MATTER :-
The concept of wave nature of matter arose from the dual character of radiations which sometimes behaves as a wave and at other time as a particle.
For example :- Radiation is considered as a wave in propagation experiments based on interference, diffraction and polarisation. These experiments prove the wave nature of radiations because they require two waves at the same position at the same time. On the other hand it is impossible for two particles to occupy the same position at same time. Radiations is considered as particle in interaction experiments like Photoelectric Effect and Compton Effect. In these experiments Radiation in the form of particle (i.e. photon) interacts with matter. However, radiations can't exhibit both particle and wave properties simultaneously. This dual nature of Radiation was not accepted because of the contradictory aspects of two nature.
1. A wave spreads out and occupies a relatively large region of space.
2. A particle occupies a definite position in the space and hence occupies very small region of space.
DE-BROGLIE HYPOTHESIS :-
According to DE-BROGLIE matter has dual ( particle as well as wave like) characteristic just like radiations.
His hypothesis about the dual nature of matter was based on the following observations :-
(a) The whole universe is composed of matter and electromagnetic radiations.
(b) The nature loves symmetry. As the radiations has dual nature, matter also posses dual nature.
According to DE-BROGLIE hypothesis a moving particle (e.g. electron, proton, neutron etc) has wave property associated with it. The waves associated with moving particles are called matter waves or pilot waves or de-Broglie waves.
Consider a photon whose energy is given by
$$E=h\nu$$
Or $$E=\frac{hc}{\lambda}$$
If a photon possesses mass (which is only by virtue of its motion i.e. it's rest mass us zero), then according to theory of relativity, it's energy is given by
$$E=mc^2$$
Now, mass of photon,
$$p=mc=\frac{h}{c\lambda}\times{c}=\frac{h}{\lambda}$$
$$\lambda=\frac{h}{p}$$
If instead of photon we consider a material particle of mass m moving with velocity $\nu$ ,then momentum of particle,
$$p=m\nu$$
Therefore, the wave associated with this moving particle is given by
$$\lambda=\frac{h}{m\nu}$$
This wavelength is called De-broglie wavelength.
There is also a experimental verification of DE-BROGLIE hypothesis that a moving particle has a wave property associated with it. This experiment namely called Davisson and Germer Experiment.
DAVISSON AND GERMER EXPERIMENT:-
The electron waves suggested by de-Broglie were first detected by Davisson and Germer were studying the reflection of electrons from a nickel target and accidentally subjected the target to such heat treatment that it was transformed into a large group of crystals because of which the reflection becomes anomalous i.e.maxima and minima appeared. They got an idea that this anomalous behaviour may be because of X-ray diffraction, suggesting thereby that electrons do behave like waves. To verify this fact, they prepared a target consisting of a single crystal of nickel.
The electron beam is produced by the electron gun. It contains a filament which is heated to dull-red, electrons are emitted by thermonic emission. These electrons are accerlated and the resulting beam is allowed to fall on a large single crystal of nickel. The electrons are scattered from the crystals in the different directions, the angular distribution being measured by electron detector.
Now, according to Bragg's Law, for maxima in the diffraction pattern
$$n\lambda=2d\sin\theta$$
From figure, $$\theta=65°,d=0.91 Angstrom$$
Assuming n=1, the de-Broglie wavelength of diffracted electron is
$$\lambda=2\times0.91\times\sin65°$$
$$=2\times0.91\times0.963$$
$$=1.65 Angstrom$$
Now, for 54 volt electrons, the de-Broglie wavelength is given by
$$\lambda=\frac{12.27}{\sqrt{V}}=\frac{12.27}{\sqrt{54}}=1.67 Angstrom$$
This, two results are in excellent agreement with each other. Hence, Davisson-Germer experiment provides direct verification of DE-BROGLIE hypothesis of the wave nature of moving particle.
