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A beam of electromagnetic radiation of intensity $6.4 \times 10^{-5}\; \mathrm{W} / \mathrm{cm}^{2}$ is comprised of wavelength, $\lambda=310 \;\mathrm{nm} .$ It falls normally on a metal (work function $\varphi=2 \;\mathrm{eV}$ ) of surface area of $1\; \mathrm{cm}^{2} .$ If one in $10^{3}$ photons ejects an electron, total number of electrons ejected in $1 \;s$ is $10^{\mathrm{x}}$.then $\mathrm{x}$ is
$\left(\mathrm{hc}=1240\; \mathrm{eV} \mathrm{nm}, 1\; \mathrm{eV}=1.6 \times 10^{-19} \;\mathrm{J}\right)$
$5$
$8$
$11$
$13$
Solution
Power incident $P=I \times A$
$\mathrm{n}=\mathrm{no} .$ of photons incident/second
$\mathrm{nE}_{\mathrm{ph}}=\mathrm{IA}$
$\mathrm{n}=\frac{\mathrm{IA}}{\mathrm{E}_{\mathrm{ph}}}$
$\mathrm{n}=\frac{\mathrm{IA}}{\left(\frac{\mathrm{hc}}{\lambda}\right)}=\frac{6.4 \times 10^{-5} \times 1}{\frac{1240}{310} \times 1.6 \times 10^{-19}}$
$\mathrm{n}=10^{+14}$ per second
since efficiency $=10^{-3}$
no. of electrons emitted $=10^{+11}$ per second.
$\mathrm{x}=11$
