Question 284: Dual Nature of Matter and Radiation

Question

A light of wavelength $\lambda$ is incident on a photosensitive surface of negligible work function. The photoelectrons emitted from the surface have de-Broglie wavelength $\lambda_1$. Then ratio $\lambda: \lambda_1{ }^2$ is
( $\mathrm{h}=$ Planck's constant, $\mathrm{c}=$ velocity of light, $\mathrm{m}=$ mass of electron)

Accepted Answer

Energy of photon : $E=\frac{h c}{\lambda}$
Kinetic energy $=K=\frac{h c}{\lambda}$
De- Broglie wavelength : $\lambda_1=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mK}}}$
$$ \begin{aligned} \lambda_1 & =\frac{\mathrm{h} \sqrt{\lambda}}{\sqrt{2 \mathrm{mhc}}} \ \lambda_1^2 & =\frac{\mathrm{h}^2 \lambda}{2 \mathrm{mhc}} \ \frac{\lambda}{\lambda_1^2} & =\frac{2 \mathrm{mc}}{\mathrm{~h}} \ 	herefore \quad \lambda_1 & : \lambda_1^2=2 \mathrm{mc}: \mathrm{h} \end{aligned} $$

Answer

$4 \mathrm{mc}: \mathrm{h}$

Answer

$\quad 2 c: h$

Answer

$2 \mathrm{mc}: \mathrm{h}$

Answer

$2 \mathrm{mh}: \mathrm{c}$

Dual Nature of Matter and Radiation

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