Debroglie’s Wave Equation
Dual Behaviour of Matter:
We studied before that the light possesses both wave and particle character i.e., dual character. de-Broglie in 1924 proposed that just like light, all the matter should exhibit both particle and wave-like properties i.e., dual behaviour.
Just like light possesses wavelength and momentum, all the matter including electrons should have wavelength and momentum.
de-Broglie gave an expression for the wavelength and momentum of all material particles.
Where ‘m’ is the mass of the particle
h=Planck’s constant = 6.626 × 10-34 Js
‘v’ is the velocity of the particle
And the product of mass and velocity is the momentum of the particle.
Momentum ) = mv
de-Broglie’s proposal was conferred after some experiments which confirmed both particle and wave nature of electron.
Significance of de-Broglie’s Relationship
de-Broglie’s relationship is not significant to the macroscopic objects. This is because macroscopic objects have large masses and if we apply de-Broglie’s relationship to large moving objects then the wavelength associated with the object is very short. Because wavelength is inversely proportional to mass.
, for moving object
This short wavelength is out of the detection limits. Therefore the term ‘wavelength’ is insignificant for macroscopic moving objects.