## 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 where of a particle or photon  For a photon and 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 about and 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 particle Suppose the alpha particle has an energy of This is the kinetic energy of the alpha particle, equal to so 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 of This 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. 