Question

A photocell is illuminated by a small bright source placed $1m$ away. When the same source of light is placed $\left(1/2\right)$ $m$ away, the number of electrons emitted by photocathode would

• A. decrease by a factor of $2$
  
  
• B. increase by a factor of $2$
  
  
• C. decrease by a factor of $4$
• D. increase by a factor of $4$

Answer 1

Answer: (D)

$I=\frac{\text{P}\text{of source}}{4\pi {\left(\text{distance}\right)}^2}=\frac{P}{4{\left(\pi d\right)}^2}$
Here, we assume light to spread uniformly in all directions.
The number of photo-electrons emitted from a surface depend on the intensity of light I falling on it. Thus the number of electrons emitted n depends directly on I. P remains constant as the source is the same.
$\therefore$ $\frac{I_2}{I_1}=\frac{n_2}{n_1}\Rightarrow \frac{P_2}{P_1}(\frac{d_1}{d_2}{)}^2=\frac{n_2}{n_1}$
$\therefore$ $\frac{n_2}{n_1}=\left(\frac{P}{P}\right){\left(\frac{1}{1/2}\right)}^2=\frac{4}{1}$ $(\because P1=P2=P)$