Question

derive the de borglie equatoin​

Answer 1

Answer:

Explanation:

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=\frac{hc}{\lambda }=λhc​    …….(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:=\frac{hc}{\lambda }=m{{v}^{2}}:=λhc​=mv2:     Then, hλ=mv\frac{h}{\lambda }=mvλh​=mv or λ=hmv=hmomentum:\lambda =\frac{h}{mv}=\frac{h}{\text{momentum}}:λ=mvh​=momentumh​: where ‘h’ is the Plank’s constant.

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