A beam of electromagnetic radiation of intensity $6.4\times10^{-5}\ \text{W/cm}^2$ is comprised of wavelength $\lambda = 310$ nm. It falls normally on a metal (work function $\varphi = 2$ eV) of surface area $1\ \text{cm}^2$. If one in $10^3$ photons ejects an electron, the total number of electrons ejected in $1$ s is $10^x$. ($hc = 1240$ eV nm, $1$ eV $= 1.6\times10^{-19}$ J), then $x$ is ______.
Numerical value type. Enter your answer.
Answer: 11
Power falling on the metal: $6.4\times10^{-5}\times1 = 6.4\times10^{-5}$ W.
Photon energy: $\dfrac{1240}{310} = 4$ eV $= 6.4\times10^{-19}$ J (greater than the work function, so emission occurs).
Photons per second: $\dfrac{6.4\times10^{-5}}{6.4\times10^{-19}} = 10^{14}$.
Electrons per second: $\dfrac{10^{14}}{10^3} = 10^{11}$, so $x = 11$.
Solution by Sreeraj P, M.Sc Physics