Louis de Broglie and the Dual Nature of Light and Matter

Not long after Einstein had declared that light was made of particles (instead of waves). Louis de Broglie further shook the foundations of physics by saying that, in effect, Einstein hadn’t gone far enough.

Einstein had declared that light (which everyone “knew” was a wave) was actually a particle. De Broglie

reflected that idea back, and said that particles (specifically electrons in his early work) had the properties of waves. His work included an equation 

λ = (h/p)

where λ=wavelength, h = Planck’s constant and p = momentum, which allows physicists to calculate the wavelength of a particle as well as the momentum (mass⋅velocity) of a wave.

On a large scale, de Broglie's work is the basis of the idea called the "Dual Nature of Light and Matter," the idea that (at a VERY small scale) matter can show wave properties and light can show particle properties. It is worth understanding that this does NOT say the electrons ARE waves, simply that we can understand electrons in some circumstances if we treat them as waves (using wave math).

As a simple human analogy I am a husband, a father and a teacher. None of those things define exactly who/what I am, but each of them can accurately describe my behavior within certain contexts. Outside of atoms (when they fly across a Crookes Tube, for instance, electron behavior can be understood (generally) as particles. Within an atom and in chemical bonds, electrons make more sense when thought of as waves.

Thus, de Broglie’s “permission” to treat electrons as waves leads directly to our current understanding of electrons in atoms.