Wave-Particle Duality

Wave Behaviour of Particles

The Belgian physicist  de Broglie (pronounced ‘de Broy’) reasoned that if waves have a particulate properties, it was reasonable to suppose that particles had wave properties.  He devised the relationship, which states that particles have wave properties.  It is the logical extension of the particulate nature of electromagnetic wave phenomena.

  He combined the following equations:

• Energy of photons:                   

E = hf

• Einstein’s mass equivalence:     

E = mc²

Therefore:

hf = mc²

Now f = c/l

So:

 mc = h/l

The term mc is mass ´ velocity, which is momentum.  We give momentum the code p.

We can rewrite the equation as  

                                    l = h/p                        or                     l = h/mv

Therefore every particle with a momentum has an associated de Broglie wavelength, even something as absurd as a car travelling at 20 m/s.

Electrons can be shown to have wave properties by the simple use of an electron diffraction tube.  A slice of carbon is placed in a beam of electrons so that the electrons diffract.

We need to note a couple of points:

• l is the de Broglie wavelength

• Strictly speaking we should count the mass and speed as relativistic.  As the speed of particles approaches the speed of light, the mass increases as kinetic energy is turned into mass.  We will not worry about this at this stage.

The wave properties of electrons have led to the development of the electron microscope, which allows magnifications much bigger than was ever possible with the light microscope.  A good light microscope can magnify up to 1000 times.  The electron microscope can magnify up to about 1 million times, and can reveal the existence of individual atoms.  The electron beams are focused by magnets just like the lenses on a microscope.