A photoelectric surface is illuminated successively by monochromatic light of Wavelength $\lambda$ and $(\lambda / 3)$. If the maximum kinetic energy of the emitted photoelectrons in the second case is 4 times that in the first case, the work function of the surface of the material is (…

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A photoelectric surface is illuminated successively by monochromatic light of Wavelength $\lambda$ and $(\lambda / 3)$. If the maximum kinetic energy of the emitted photoelectrons in the second case is 4 times that in the first case, the work function of the surface of the material is ( $\mathrm{h}=$ Planck's constant, $\mathrm{c}=$ speed of light $)$

Aicharya · Accepted Answer

$\begin{aligned} & \quad 1^{	ext {st }} 	ext { case: } \ & \mathrm{E}_0=\frac{\mathrm{hc}}{\lambda}-\phi...(i) \ & 2^{	ext {nd }} 	ext { case: } \ & 4 \mathrm{E}_0=\frac{\mathrm{hc}}{\frac{\lambda}{3}}-\phi ...(ii)\ & 	herefore \quad \frac{4 \mathrm{E}_0}{\mathrm{E}_0}=\frac{\frac{3 \mathrm{hc}}{\lambda}-\phi}{\frac{\mathrm{hc}}{\lambda}-\phi} \ & \frac{4 \mathrm{hc}}{\lambda}-4 \phi=\frac{3 \mathrm{hc}}{\lambda}-\phi \ & \phi=\frac{\mathrm{hc}}{3 \lambda} \end{aligned}$ $\ldots[$ From(i) and (ii) $]$

A photoelectric surface is illuminated successively by monochromatic light of Wavelength $\lambda$ and…

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