Matter Waves and Electron Microscopes - A2 Physics - AQA

Matter Waves

Electrons are considered to travel as matter waves, which are not composed of matter despite their name.  It is instead to do with probability.  Where the amplitude is greater, there is a greater probability of finding an electron.   It is also true of photons.  We can no longer think in quantum physics of particles like electrons being solid point masses like lead shots. Its wave function is extended over an extended region of space rather than being at a single point.

This is quantified by complex mathematical functions that are way beyond what we need to know.  Werner Heisenberg was considering the matter waves of electrons, when he proposed his uncertainty principle.  In effect, the closer you are to pinning down an electron the harder it is to pin down. (Heisenberg was a brilliant theoretical physicist, but useless at practical physics.)

These difficult concepts in quantum physics enable us to explain tunnelling, which we will look at next.

We know that an electron can have discrete energy levels.

According to classical physics, the electron can only be at energy level 1 or 2.  It will not have enough energy to jump over the energy hill.

If we adopt the quantum mechanics idea, where the bigger the amplitude of a matter wave, the greater the probability of finding the electron, we get this:

There is a small but finite probability of finding the electron on the other side of the energy hill.  It seems to have tunnelled through the energy hill, and this effect is called quantum tunnelling.  It is impossible to explain this by classical physics, but (comparatively) easy to use quantum physics which is based on probability.

 "The principle of tunnelling is based on the wave nature of particles.  Light can be seen through a thin metal film because the amplitude of the light waves is not reduced to zero by the passage of the light in the film.  In the same way, the amplitude of matter waves in a barrier does not become zero if the barrier is sufficiently narrow.  This process…