The second step was a bold proposal that subatomic particles, specifically electrons, have wave properties. Particles are described by their momenta (mass times speed). Waves are described by their wavelengths. If particles have wave properties, there should be a connection between momentum and wavelength. This connection, which was discovered by Louis de Broglie in 1923 – and won him a Nobel Prize in Physics in 1929 – states that if you divide the Planck constant by a particle’s momentum (in scientific units), you’ll get its wavelength in meters. The de Broglie relation is universal; it applies to any and all particles and waves. Any particle that shows wave properties obeys the laws of the quantum theory.
How do you know if something has wave property? You look for its diffraction. What is diffraction? It is the bending of wave as it passes through an opening. For example, when a door is open – in a wall so thick that no sound is heard on the other side if the door (also thick) is closed – and you talk on one side of the door, a person on the other side will hear you even if (s)he is not standing directly in front of the door. We say that sound wave diffracts (bends) through the opening.
Light is also a wave, an electromagnetic wave. However, if you pass a beam of light (from a flashlight, for example) through the door opening, it will not diffract: the person on the other side must be directly in the straight path of the light beam to be able to see it. Now the question is, why does sound wave diffract through a doorway but light wave doesn’t? The answer is
In order for a wave to diffract, it must have a wavelength that is not too much smaller that the opening through which it passes.
A typical sound wave has a wavelength of around a meter or so. A doorway is also about a meter or so wide. So, sound wave diffracts. On the other hand, a typical light wave has a wavelength of about a millionth of a meter (a micrometer), much much smaller than the opening. So, light does not diffract through a doorway. But it does diffract through a very small hole created in a laboratory setting – that’s how in the early 19th century, Thomas Young showed that light was a wave (he actually used another property of the wave called interference, but the difference between interference and diffraction is not essential for our discussion).