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Wave Optics

Question

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

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Solution

De-Broglie wavelength of a photon is,

λ = \frac{h}{p}

Momentum of a photon,

p = \frac{hv}{c}

Hence,

λ = \frac{h}{\frac{hv}{c}} = \frac{c}{v}

which proves that it is same as the wavelength of electromagnetic radiation.