In 1924 Louis-Victor de Broglie hypothesized that if the wave length of light (Lambdalight) could be determined by the energy contained in a particle (photon) of light, according to the relation:
De Broglie Wavelength for Electrons
Lambdalight = h.c / Ephoton
then perhaps physical particles such as electons could have a wavelength determined by their energy, as well. Note that h is Planck's Constant and c is the speed of light.
To be able to compare like quantitues between electrons and photons, he recast the above expression for Lambdalight in terms of the momentum of a photon. Relativity Theory gives the momentum (p) of a photon as:
pphoton = Ephoton / c
Substituting the resulting expression for Esub>photon into the above expression for Lambdalight gives:
Lambdalight = h / pphoton
De Broglie then used this expression to calculate a wave length for an electron subsituting 'm.v' for the momentum 'p' where 'm' is the mass of the electron and 'v' is the electron velocity.
Lambdaelectron = h / (m.v)
In 1927 at Bell Labs, Clinton Davisson and Lester Germer demonstrated that electrons did indeed create a diffraction patttern consistent with their De Broglie wavelength. They did this by firing slow-moving electrons at a crystalline nickel target and then measuring the angular dependence of the density of the deflected electrons .