DE-BROGLIE HYPOTHESIS MATTER WAVE

• MATTER WAVE :-

         In 1924 de-broglie proposed that matter also has a dual nature just like radiation. His hypothesis about the dual nature of matter was base on following observations.

  I) The whole universe is composed of matter and electromagnetic radiation.

 II) The nature loves symmetry . As the radiation has dual nature, matter should also possess dual nature.

   

     According to de-broglie, a wave is associated with every moving material particles. These waves are called de-broglie waves or matter waves.

    According to quantum theory, energy of a photon is given bye

                 E= hv

 Where h is Planck's constant and v is frequency of radiation.
Relativistic energy of a particle is given by

Sine rest mass of photon is zero i.e mo= 0
Then  E= pc
           hv= pc
 Momentum of photon p= hv/ c
Or
(c=hλ)
Where λ is wave length of radiation.
       λ= h/p............(1)
If instead of photon , we consider a material particles of mass m is moving with velocity v, then the momentum of the particles.
   P= mv
Putting this value in eq( 1) we get
     λ= h/mv or,

This wave length λ is called de- Broglie wavelength.