Question

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

Answer 1

The momentum of a photon having energy (hv) is given as:
\(p=\frac{hv}{c}=\frac{h}{λ}\)
\(λ=\frac{h}{p}.......(i)\)
Where,
λ=Wavelength of the electromagnetic radiation
c=Speed of light
h=Planck’s constant De Broglie wavelength of the photon is given as:
\(λ=\frac{h}{mv}\)
But \(p=mv\)
\(∴λ=\frac{h}{p}.........(ii)\)
Where, m=Mass of the photon
v=Velocity of the photon
Hence,it can be inferred from equations (i) and (ii) that the wavelength of the electromagnetic radiation is equal to the de Broglie wavelength of the photon.