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^-9)m`(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 2.0e V.

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. `