1. Louis de Brogue extended the concept of dual nature of light to all forms of matter. To quantify this relation, he derived an equation for the wavelength of a matter wave.
2. He combined the following two equations of energy of which one represents wave character (hu) and the other represents the particle nature (mc2).
Planck’s quantum hypothesis:
E = hv ….(1)
Einsteins mass – energy relationship:
E = mc2 …(2)
From (1) and (2)
hv = mc2
hc/λ = mc2
∴ λ = h/mc2 …(3)
The equation (3) represents the wavelength of photons whose momentum is given by mc. (Photons have zero rest mass).
3. For a particle of matter with mass m and moving with a velocity y, the equation (3) can be written as
λ = h/mc …(4)
4. This is valid only when the particle travels at speed much less than the speed of Light.
5. This equation implies that a moving particle can be considered as a wave and a wave can exhibit the properties of a particle (i.e momentum).
6. Significance of de Brogue equation: For a particle with high linear momentum, the wavelength will be too small and cannot be observed. For a microscopic particle such as an electron, the mass is 9.1 x 10-31 kg.
Hence the wavelength is much larger than the size of atom and it becomes significant.