Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).

The momentum of a photon having energy (hv) is given by the elation:

(i)

Where,

wavelength of the electromagnetic radiation

speed of light

Planck’s constant

De Broglie wavelength of the photon is given by the relation:

But,

Therefore, (ii)

Where, mass of the photon

velocity of the photon

The wavelength of electromagnetic radiation and the de Broglie wavelength of the photon are same, according to equations (i) and (ii).