Show that the wavelength of electromagnetic ...

NCERT Class XII Chapter
Dual Nature of Radiation and Matter
Questions With Solutions

Question : 18 of 37

Marks: +1, -0

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

Solution:

For a photon, de Broglie wavelength, λ =

\frac{h}{p}

For an electromagnetic radiation of frequency υ and wavelength λ′(= c/υ),

Momentum, p =

\frac{E}{c}

\frac{hv}{c}

or p =

\frac{h}{c} \cdot \frac{c}{\lambda'}

\frac{h}{\lambda'}

Then , λ' =

\frac{h}{p}

= λ

Thus the wavelength λ′ of the electromagnetic radiation is the same as the de Broglie wavelength λ of the photon.

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