Question

A photocell is illuminated by a small bright source placed $1m$ away. When the same source of light is placed $\frac{1}{3}m$ away, the number of electrons emitted by photo cathode would increase by a factor of ______

Answer 1

Answer: 9

For a fixed frequency, photoelectric current is directly proportional to intensity and intensity is inversely proportional to square of the distance.
$\therefore$ Number of photoelectrons $\propto \frac{1}{(\text{ distance }{)}^2}$
$\frac{N_1}{N_2}=\frac{d_2^2}{d_1^2}$
$\therefore N_2=N_1\times {\left(\frac{d_1}{d_2}\right)}^2$
$=N_1\times {\left(\frac{1}{1/3}\right)}^2$
$=9N_1$