What is the De Broglie equation?

The de Broglie equation is ##lambda_(dB) = h/p## where ##lambda_(dB)## is the de Broglie wavelength, ##h## is , and ##p## is the momentum of the particle. The de Broglie hypothesis tells you about the wave-particle duality of matter.

It can also be written equivalently as ##nu_(dB) = E/h## where ##nu_(dB)## is the frequency, ##E## is the energy, and ##h## is Planck's constant.

De Broglie came to this hypothesis by borrowing ideas from Planck's quantization of energy of light and Einstein's relativity. ## E_(light) = h nu = cp## where ##c## is the speed of light.

Also, recall ##lambda nu = c##

After manipulating the equation, you find ##h/p = c/nu = lambda## which is a relation that holds for light.

De Broglie hypothesized that this relation could also hold for particles, and it turns out that his guess was right!