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

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Class 12 Physics
CBSE and UP Board
Dual Nature of Radiation and Matter
Chapter-11 Exercise 11.18
NCERT Solutions for Class 12 Physics Chapter 11 Question-18

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1 Answer

  1. The momentum of a photon having energy (hv) is given as:

    p = hv/c = h/λ

    => λ = h/p

    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 = h/mv

    But , p=mv,  therefore

    λ = h/p

    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.

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