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

Explanation

The momentum of a photon having energy (hv) is given as : `p=(hc)/c=h/lambda`
`lambda=h/p` …(i)
Where , `lambda`=Wavelength of the electromagnetic radiation
c=speed of light
h=Planck's constant
De Broglie wavelength of the photon is given as : `lambda=h/(mv)`
But p=mv
`lambda=h/p` ...(ii)
Where,
m=Mass of the photon
v=velocity of the photon
Hence, it can be inferred from equatins (i) and (ii) that the wavelength of the electromagnetic radiation is equal to the de-Broglie wavelength of the photon .