Ncert Exercises & Solutions

Question 11.18:
Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).

Hint: \(\lambda=\frac{h}{p}\)

Step 1: Find the wavelength of the electromagnetic radiation.
The momentum of a photon having energy (hv) is given as

p = \frac{h v}{c} = \frac{h}{λ}

\Rightarrow λ = \frac{h}{p}

...(i)
Step 2: Find the de Broglie wavelength of the photon
De Broglie wavelength of the photon is given as

λ = \frac{h}{m v}

But p = mv, therefore

\Rightarrow λ = \frac{h}{p}

...(ii)
Step 3: Compare the wavelength of electromagnetic radiation with the de Broglie wavelength of the photon
Hence, it can be inferred from equations (i) and (i) that the wavelength of the electromagnetic radiation is equal to the de Broglie wavelength of the photon.

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