Question

A photocell is illuminated by a small bright source placed $1 \, m$ 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 $ $\frac{I_{2}}{I_{1}}=\frac{n_{2}}{n_{1}}\Rightarrow \frac{P_{2}}{P_{1}}\left(\right. \frac{d_{1}}{d_{2}} \left.\right)^{2}=\frac{n_{2}}{n_{1}}$
$\therefore $ $\frac{n_{2}}{n_{1}}=\left(\frac{P}{P}\right)\left(\frac{1}{1/2}\right)^{2}=\frac{4}{1}$ $\left(\right.\because P1=P2=P\left.\right)$