A point source of monochromatic light of `1.0 mW` is placed at a distance of `5.0 m` from a metal surface. Light falls perpendicularly on the surface. Assume wave theory of light to hold and also that all the light falling on the circular area with radius `=1.0 xx 10^-9m`(which is few times the diameter of an atom) is absorbed by a single electron on the surface. Calculate the time required by the electron to receive sufficient energy to come out of the metal if the work function of the metal is `2.0eV`.

Explanation

The energy radiated by the light source per
second is 1.0mJ. This energy is spread over the total solid angle `4pi`. The
solid angle subtended at the source
by the circular area mentioned is
` d(Omega)= (dA/(r^2))= ((pi xx (1.0 xx (10^-9)m))^2/(5.0m)^2) = (pi/25) xx (10^-18) sr.`
Hence the energy heading towards the circular area per
second is
` (d Omega/ 4pi) (1.0mJ) = (10^-20)mJ.`
` The time required for accumulation of 2.0e V of energy
on this circular area is
` (t=(2.0 xx 1.6 xx (10^-19)J)/(10^-20)mJ(s^-1)) = 3.2 xx (10^4)s = 8.8 hours. `