Question

A light beam of wavelength $400nm$ is incident on a metal plate of work function $2.2eV$. A particular electron absorbs a photon and makes some collisions before coming out of the metal. Assuming that $10\%$ of the instantaneous energy is lost to the metal in each collision, find the minimum number of collisions the electron can suffer before it becomes unable to come out of metal. (Use $hc=12400eV\dot{A}$)

Answer 1

Energy of a photon of 400nm will be $E=\frac{1240eVnm}{400nm}=3.1eV$

Energy after first collision $0.9E$

energy after second collision $09\times 0.9E=0.81E$

energy after $n^{th}$ collision will be $(0.9{)}^{n}E$

Electron will not be able to come out if $(0.9{)}^{n}E$ becomes less than $2.2eV$ so $n=4$ will be minimum required collision to stop it from ejection.