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 (mc^{2}).

**Planck’s quantum hypothesis: **

E = hv ….(1)

Einsteins mass – energy relationship:

E = mc^{2} …(2)

From (1) and (2)

hv = mc^{2}

hc/λ = mc^{2}

∴ λ = h/mc^{2 }…(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.