The Faster Things Move, The Smaller They Get

If there is a single equation that summarises the grand unification of quantum and classcal physics, it has to be De Broglie's equation


of a particle or photon

For a photonand for a particle with mass(at much smaller speeds than the speed of light).

Consider what this means for an alpha particle approaching a gold atom. The diameter of a gold atom is aboutand the size of an alpha particle may be consider to be related to the wavelength. If the wavelength is small then so is the particle.

For an alpha particleSuppose the alpha particle has an energy ofThis is the kinetic energy of the alpha particle, equal toso that

The wavelength of wave associated with the alpha particle is

This is about the same size as a gold atom.

Suppose now that the alpha particle has an energy 10 MeV. The procedure above gives a speed of 2200000 m/s and a wavelength ofThis is much smaller than the size of an atom – about the same size as a nucleus. The alpha particle will now see a gold atom as mostly empty space and will be much more likely to pass through undeflected by the nucleus.