A metal plate is placed 5m from a monchromatic ligth
soure whose power output is `10^(-3)`W. Consider that a given ejected
photoelectron may collect its energy from a circular area of the plate as large as
ten atomic diameters `10^(-9)` m in radius. The energy required to remove an electron through the metal surface is about 5.0 eV. Assuming light to be a
wave, how long would it take for such a 'target' to soak up this much energy
from such a light source.

Answer

B

Explanation

The target are is `S_1 = pi (10^(-9)^2 = pixx10^(-18) m^2`. The area of a 5 m sphere centered
on the light source is, `S_2 = 4pi(5)^2 = 100pi m^2`. Thus,if the light source radiates uniformly in all
directions the rate P at which energy falls on the target is given by
`P = (10^(-3 watt) ((S_1)/(S_2)) = (10^(-3) ((pixx10^(-18))/(100xxpi)) = 10^(-23) J//s`
Assuming that all power is absorbed, the required time is
`t=((5eV)/(10^(-23) J//s)) ((1.6xx10^(-19) J)/(1 eV)) ~~20 h`