Question
A photocell is illuminated by a small bright source placed $$1 m$$ away. When the same source of light is placed $$\frac{1}{2}m$$ away, the number of electrons emitted by photocathode would
A.
increase by a factor of 4
B.
decrease by a factor of 4
C.
increase by a factor of 2
D.
decrease by a factor of 2
Answer :
increase by a factor of 4
Solution :
$$\eqalign{
& I \propto \frac{1}{{{r^2}}};\frac{{{I_1}}}{{{I_2}}} = {\left( {\frac{{{r_2}}}{{{r_1}}}} \right)^2} = \frac{1}{4} \cr
& {I_2} \to 4\,{\text{times}}\,{I_1} \cr} $$
When intensity becomes 4 times, no. of photoelectrons emitted would increase by 4 times, since number of electrons emitted per second is directly proportional to intensity.