Question

A photocell is illuminated by a small bright source placed $1 \,m$ 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

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} $
$=9 \,N _{1}$