Question

derive De Broglie equation​

Answer 1

Complete step by step answer: We know that electromagnetic radiation exhibits the dual nature of a particle and wave. Microscopic particles like electrons also possess this type of dual nature.

Let us derive the de-Broglie equation:

Very low mass particle moving at speed less than that of light behaves like a particle and wave. De-broglie derived an expression relating the mass of such smaller particles and its wavelength.

Plank’s quantum theory relates the energy of an electromagnetic wave to its wavelength or frequency.

E=hν=hcλ ………..(1)

Einstein related the energy of particle matter to its mass and velocity, as E = mc2 ………(2)

As the smaller particle exhibits dual nature, and energy being the same, de-Broglie equated both these relations for the particle moving with velocity ‘V’ as,

E = hcλ = mv2:Then,hλ = mv

λ=hmv = hmomentum, where ‘h’ is the plank’s constant.

This equation relating the momentum of a particle with its wavelength is the de-Broglie equation and the wavelength calculated using this relation is the de-Broglie wavelength.