WAVE - PARTICLE DUALITY

Wave and particle character of electron :-

(DUAL CHARACTER)

1) Einstein, suggested, in 1905's, that light has a double (dual) character ; as particle and also as wave ;

2) Louis de broglie proposed that the matter also has a dual character ; as particle and as wave.

3) De broglie was got award the Noble Prize in 1929's

4) In Bohr's theory, electron is treated as a particle. But de broglie's theory suggests that matter and therefore, electron also, has a dual character, both as a material particle and as a wave.

5) He derived an expression for calculating the wave length λ of a particle of mass 'm' moving with velocity 'v' according to which is,

          λ =   h   ................................. (1) 

                mv

The above equation is known as the de broglie equation.

The de broglie equation we can be easily derived by using the mass energy and relationship, 

          E = mc²   ..........................(2)

Equating with this energy with the energy of a photon. We have

                 hυ = mc²

Since υ = c/λ

               hc/λ = mc²

               h/λ  = mc

                  λ = h/mc

Replacing 'c' by the velocity of the electrons V, we have

                λ = h/mv = h/p

Where, 

                  ' p' is called as the momentum of the particle.