Basic Modern Physics
3.0 Wave Particle Duality
3.0 Wave Particle Duality
It states that matter has both wave as well as particle nature.(de Broglie Hypothesis). Waves associated with matter is known as matter waves. It is given by $${\lambda _{(matter\ wave)}} = \frac{h}{{mv}}$$ where $m$=mass and $v$=velocity of the particle. It is also known as de-Broglie wavelength.
The propagation of light is governed by its wave properties, whereas the exchange of energy between light with matter is governed by its particle properties. Similarly, if a charge $q$ is accelerated by a potential difference of $V$ it gains a kinetic energy of $KE = qV$. So we can write $$\lambda = \frac{h}{{mv}} = \frac{h}{p} = \frac{h}{{\sqrt {2Km} }} = \frac{h}{{\sqrt {2qVm} }}$$
