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(D) The intensity of light $I$ at a distance $d$ from a point source is given by $I \propto \frac{1}{d^2}$.Since the number of photoelectrons emitted

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Increase by a factor of $4$

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(D) The intensity of light $I$ at a distance $d$ from a point source is given by $I \propto \frac{1}{d^2}$.Since the number of photoelectrons emitted per second is directly proportional to the intensity of the incident light,we have $N \propto I$.Therefore,$N \propto \frac{1}{d^2}$.When the distance is changed from $d$ to $\frac{d}{2}$,the new number of photoelectrons $N'$ is given by $N' \propto \frac{1}{(\frac{d}{2})^2} = \frac{4}{d^2}$.Comparing $N'$ with $N$,we get $N' = 4N$.Thus,the number of electrons emitted increases by a factor of $4$.

$A$ photocell is illuminated by a small bright source placed $d \; m$ away. When the same source of light is placed $\frac{d}{2} \; m$ away,the number of electrons emitted by the photocathode would

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