Question

derive de brogile wavelength. please answer this question my friends... ​

Answer 1

Answer:

Very low mass particles 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  =\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 = =\frac{hc}{\lambda }=m{{v}^{2}}:=λhc=mv2:     Then, \frac{h}{\lambda }=mvλh=mv or \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.