A light beam of wavelength 400 nm is incident on a metal plate of work function 2.2 eV.
(a) A particular electron absorbs a photon and makes two collisions before coming out of the metal. Assuming that 10% of the extra energy is lost to the metal in each collision, find the kinetic energy of this electron as it comes out of the metal.
(b) Under the same assumptions, find the maximum number of collisions the electron can suffer before it becomes unable to come out to the metal.
Given, wavelength 
Work function 
(a) We know that energy of photon 
As it is given that 10% extra energy is lost to the metal
In each collision
∴ Energy lost after first collision 
Now, energy lost after secomd collision 
∴ total energy lost in collision 
Hence, Kinetic energy of photoelectron = 
(b) For third collision energy lost =0.31eV
Hence, we see that energy lost in third collision =kinetic
energy of photoelectron
∴ In third collision it just comes out of the metal
and in fourth collision it is unable to come out
of the metal.
∴ Maximum number of collisions required =4.