The de Broglie hypothesis
Cont’d from “Energy of an electron”With the breakthrough of quantum physics, de Broglie (pronounced, “de broy”) worked to relate the quantum-like and wave-like properties of particles. He typified this by expressing the energy E of a photon in terms of its wavelength λ, which soon became known as the de Broglie wavelength.
E = hν = hc/λ
where h is Planck’s constant, ν is the wave frequency and c is the speed of light. He next proposed the momentum p of a particle can be given by
p = h/λ
Furthermore, he suggested this would apply to other quanta, including electrons. If relativistic effects did not apply he would be completely correct, however we know a particle with mass has a frequency ν ≠ c/λ since its velocity v ≪ c. This was confirmed by Davisson and Germer who, by inspecting the diffraction pattern of electron waves reflected off a plate of nickel crystal, quantitatively proved that
d·sin θ = n·λ
where d is the separation distance of two atoms in the crystal, θ is the reflected angle from the initial beam and n is the maxima number from the initial maxima n0. In comparison, the equation for de Broglie wavelength showed the quantitative wavelength of the electron beam to be very close to the expected theoretical value, within 1% error due to relativistic effects, thus proving the fundamental basis for de Boglie’s hypothesis and earning him a Nobel Prize in physics just 3 years later!