Explain the particle-wave (dual) nature of matter.

(N/A) The dual nature of matter and radiation suggests that they exhibit both wave-like and particle-like properties depending on the experimental conditions.
$1$. Wave Nature: Phenomena such as interference,diffraction,and polarization demonstrate that light and matter particles (like electrons) behave as waves.
$2$. Particle Nature: Phenomena such as the photoelectric effect,Compton effect,and black-body radiation demonstrate that light and matter behave as discrete packets of energy called quanta or photons.
$3$. De Broglie Hypothesis: Louis de Broglie proposed that every moving particle of matter is associated with a wave,known as the matter wave,with a wavelength given by $\lambda = h/p$,where $h$ is Planck's constant and $p$ is the momentum of the particle.
Thus,matter exhibits a dual nature,behaving as a particle in terms of energy exchange and as a wave in terms of propagation.