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Physics · 2026 · 3 marks
CBSE 2026 · Region 4 · Set 1 · Q26
(a) Explain how the dual aspect of matter is evident in the de Broglie relation. (b) Radiation of wavelength λ is incident on a photosensitive…
(a)
Explain how the dual aspect of matter is evident in the de Broglie relation.
(b)
Radiation of wavelength $\displaystyle \lambda$ is incident on a photosensitive surface. Find the de Broglie wavelength of electrons emitted from the surface. Assume that the work function of the surface is negligible.
Marking-scheme solution
(a)
According to the de Broglie relation, the wavelength $\displaystyle \lambda$ associated with a particle of momentum p is given as $\displaystyle \lambda=\dfrac{\mathrm{h}}{\mathrm{p}}=\dfrac{\mathrm{h}}{\mathrm{mv}}$
$\displaystyle \lambda$ is the characteristic of a wave whereas momentum p is a typical characteristic of a particle. The de Broglie relation connects the two characteristics.
(b)
Kinetic energy of the electron $\displaystyle =\dfrac{1}{2} m v^{2}=\dfrac{\mathrm{h} c}{\lambda}$
$\displaystyle v=\sqrt{\dfrac{2 \mathrm{h} c}{m \lambda}}$
de Broglie wavelength of the electron $\displaystyle \left(\lambda^{\prime}\right)=\dfrac{\mathrm{h}}{\mathrm{mv}}=\dfrac{\mathrm{h}}{m \sqrt{\dfrac{2 \mathrm{hc}}{m \lambda}}}$
$\displaystyle \lambda^{\prime}=\sqrt{\dfrac{\mathrm{h} \lambda}{2 m c}}$
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