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Question

A light beam of wavelength 400 nm is incident on a metal plate of work function 2.2 eV. 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=12400 eV ˙A)

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Solution

Energy of a photon of 400nm will be E=1240eVnm400nm=3.1eV
Energy after first collision 0.9E
energy after second collision 09×0.9E=0.81E
energy after nth collision will be (0.9)nE
Electron will not be able to come out if (0.9)nE becomes less than 2.2eV so n=4 will be minimum required collision to stop it from ejection.

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