## Wave Particle Duality

Even after so much of comprehensive analysis Bohr failed to deliver a well suited model although many of the postulates given by Bohr are still true. Now more focus shifted to the nature of electron. We already know that Planck and Einstein proposed that EM waves have some particle nature associated with them that is why their energy was found to be quantized. Somehow the behaviour of electrons lead scientists to think the other way round as well. That is, if waves can have particle nature then even particles may be associated with wave like properties. This is exactly what De Broglie proposed and Heisenberg followed it with his uncertainty principle and based on these new theories the modern Quantum Mechanical Model emerged.

### Wave Particle Duality: De-Broglie Concept

De Broglie proposed that particles in motion should have some wave nature associated with them. The main reason for this was the symmetry in nature. If waves have particle nature then there is no reason why particles cannot possess wave nature. This was confirmed when a beam of electrons was found to exhibit diffraction on being passed through a small slit. Diffraction is a property exhibited by waves and that’s why it was assumed that electrons are associated with wave nature. De Broglie extended this theory to the whole matter and introduced the concept of “Matter Waves”. He even proposed an expression to calculate the wavelength associated with a particle in motion.
This equation is called De-Broglie Equation:
λ = h/p
Where p is the linear momentum of a particle. This equation clearly indicates that for particles of smaller mass this wavelength will have a significantly large value but for large macroscopic particles the wavelength will diminish and will not carry much of a significance. Let’s compare two cases:
1. An electron moving with a velocity of 106 m/s
2. A cricket ball (m=0.5 kg) moving with a velocity of 10 m/s
Substituting the linear momenta of the above two matter particles in the De Broglie equation we obtain the De Broglie wavelength for the two.
For the electron, λ = 7.2 × 10-10 m
For the cricket ball, λ = 1.325 × 10-34 m
The wavelength of the ball seems to be very small as compared to the dimensions of the macroscopic world of which the ball is a part and this cannot be detected. Even for the electron the value of the wavelength is very small but electron is a microscopic particle and this value is comparable to the radius of an atom! That’s why De-Broglie wavelength is highly significant in this case.