Question 300: Dual Nature of Matter and Radiation

Question

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 $)$

Accepted Answer

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

Answer

$\frac{\mathrm{hc}}{\lambda}$

Answer

$\frac{\mathrm{hc}}{2 \lambda}$

Answer

$\frac{\mathrm{hc}}{3 \lambda}$

Answer

$\frac{3 \mathrm{hc}}{\lambda}$

Dual Nature of Matter and Radiation

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