Question 365: Dual Nature of Matter and Radiation

Question

Photoelectrons are emitted when photons of energy $$4.2 ~\mathrm{eV}$$ are incident on a photosensitive metallic sphere of radius $$10 \mathrm{~cm}$$ and work function $$2.4 ~\mathrm{eV}$$. The number of photoelectrons emitted before the emission is stopped is
$$\left[\frac{1}{4 \pi \epsilon_0}=9 	imes 10^9ight.$$ SI unit; $$\left.\mathrm{e}=1.6 	imes 10^{-19} \mathrm{C}ight]$$

Accepted Answer

$$\mathrm{hv}=4.2 \mathrm{~eV}, \omega_0=2.4 \mathrm{~eV},(\mathrm{KE})_{\max }=4.2-2.4=1.8 \mathrm{~eV}$$
The electrons will not be able to escape from the surface when its potential becomes $$1.8 \mathrm{~V}$$.
$$\begin{aligned}
\mathrm{V} & =\frac{1}{4 \pi \epsilon_0} \frac{\mathrm{q}}{\mathrm{r}} \
	herefore 1.8 & =9 	imes 10^9 	imes \frac{\mathrm{q}}{0.1} \
	herefore \mathrm{q} & =2 	imes 10^{-8} \mathrm{C} \
	herefore \mathrm{ne} & =\mathrm{q} \
\mathrm{n} & =\frac{\mathrm{q}}{\mathrm{e}}=\frac{2 	imes 10^{-11}}{1.8 	imes 10^{-14}}=1.25 	imes 10^8
\end{aligned}$$

Answer

$$1.25 	imes 10^6$$

Answer

$$1.25 	imes 10^2$$

Answer

$$1.25 	imes 10^8$$

Answer

$$1.25 	imes 10^4$$

Dual Nature of Matter and Radiation

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