Wave theory of electromagnetic radiations explained the phenomenon of interference, diffraction and polarization of light.
On the other hand, Quantum theory of electromagnetic radiations successfully explained the photoelectric effect, Compton effect, black body radiation e.t.c.
It means that radiation sometimes behaves as a wave and sometimes as a particle.
Wave Nature of Matter(Particles): De-Broglie Hypothesis:-
In 1924 De-Broglie put a hypothesis that nature is symmetrical. If radiations(light) behaves as wave and particle nature then matter(particles) can also behaves as wave.
“Every moving particle have a wave associated with it,, He got Nobel Prize for this.
According to de-Broglie, a wave is associated with moving material particle which controls the particle in every respect. The wave associated with moving material particle is called matter wave or De-Broglie wave whose wavelength is called De-Broglie wavelength.
Derivation:
* Matter wave like electromagnetic wave can travel in vacuum and hence they are not mechanical waves.