CBSE 2026 · Region 4 · Set 1 · Q26 · 3 marks
(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.
(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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CBSE Class 12 Physics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.