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!