## Sunday, 27 February 2011

### Wave-particle duality

Compton scattering: the phenomenon that when the incident photon hits a free electron, the free electron will be scattered and change its direction, with photon with lower frequency bounced away. This gives the evidence that photon can exist in matter form.
Recall the wave nature of light: diffraction (single slit) and interference (Young's double slit)
Particle nature of light: photoelectric effect and Compton scattering.
Einstein states that E=pc, where E is the energy of the photon, p is its momentum and c is the speed of light. Rewrite the equation: E = pc = pfλ = hf, we have the wavelength-momentum relation: p = h/λ. This describes the particle characteristic of photon.
In 1924, de Broglie claims that λ = h/p in his doctorial thesis called de Broglie relation. The corresponding λ is called De Broglie wavelength. This describes the wave nature of a matter which is revolutionary at the time, which awards him the Nobel Prize in Physics in 1929.
Students should note that though p = h/λ and λ = h/p is mathematically equivalent but they should be proved independently since these two equation describes different things. Of course, their validity has been no doubt after some experimental effort, but this is beyond the scope of this set of note.
No matter wave behavior is observed in daily life because their wavelength is far too small to be observed. (smaller than 10-35m). However electrons are proved to have wave nature in experiment: a fast-moving electron has wavelength about 10-10m while the interatomic separation is about the same. Interference pattern was observed when electron beam hits nickel foil and reflect with different angles. The graph of frequency of electrons VS deflected angle shows several maxima and minima. Very soon, Sir George Thomson (son of J.J.Thomson) created another experiment which hits the electron beam on a metal foil and the scattered electron beams interfere. Rings are shown on the fluorescent screen, which is similar to result by X-rays. The process that "electron shown on fluorescent screen" is a particle behavior, so this experiment actually shows the duality nature of electrons.
Double-slit experiment of electrons was also done to show the wave behavior of electrons. Some small molecules like C60's wave behavior have been experimentally verified too.