Dual Character (Particle And Wave Character Of Matter And Radiation)

In case of light some phenomenon like diffraction and interference can be explained on the basis of its wave character. However, the certain other phenomenon such as black body radiation and photoelectric effect can be explained only on the basis of its particle nature. Thus, light is said to have a dual character. Such studies on light were made by Einstein in 1905.

Louis de Broglie, in 1924 extended the idea of photons to material particles such as electron and he proposed that matter also has a dual character-as wave and
as particle.

Derivation of de-Broglie equation

The wavelength of the wave associated with any material particle was calculated by analogy with photon.

In case of photon, if it is assumed to have wave character, its energy is given by

E = hν

(i) (according to the Planck’s quantum theory)

where ν is the frequency of the wave and ‘h’ is Planck’s constant

If the photon is supposed to have particle character, its energy is given by

E = mc²

(ii) (according to Einstein’s equation)

where ‘m’ is the mass of photon, ‘c’ is the velocity of light.

By equating (i) and (ii)

hν = mc²

But ν = c/λ

hc/λ = mc2

(or) λ = h /mc

The above equation is applicable to material particle if the mass and velocity of photon is replaced by the mass and velocity of material particle. Thus for any material particle like electron.

λ = h/mv (or) λ= h/p

where mv = p is the momentum of the particle.