Two metallic plates $A$ and $B$, each of area $5 imes 10^{-4} \mathrm{~m}^2$, are placed parallel

Question

Two metallic plates $A$ and $B$, each of area $5 	imes 10^{-4} \mathrm{~m}^2$, are placed parallel to each other at a separation of 1 cm . Plate $B$ carries a positive charge of $33.7 	imes 10^{-12} \mathrm{C}$. A monochromatic beam of light, with photons of energy 5 eV each, starts falling on plate $A$ at $t=0$ so that $10^{16}$ photons fall on it per square metre per second. Assume that one photoelectron is emitted for every $10^6$ incident photons. Also assume that all the emitted photoelectrons are collected by plate $B$ and the work function of plate $A$ remains constant at the value 2 eV . The number of photoelectrons $\left(	imes 10^7ight)$ emitted upto $t=10 \mathrm{~s}$.

Professor PC Thomas Classes · Answer

(c) : Area of each plate $=5 	imes 10^{-4} \mathrm{~m}^2$ Separation between plates $=1 \mathrm{~cm}=10^{-2} \mathrm{~m}$ $$ \frac{	ext { Photons incident }}{	ext { area × time }}=10^{16}, t=10 \mathrm{~s} $$ $	herefore \quad$ No. of photons incident $=10^{16} 	imes$ area × time $$ =10^{16} 	imes\left(5 	imes 10^{-4}ight) 	imes 10=5 	imes 10^{13} $$ ∴ $\quad$ Required number of photoelectrons emitted $$ =\frac{5 	imes 10^{13}}{10^6} $$ Number of photoelectrons $=5 	imes 10^7$