Question

A photoelectric cell is illuminated by a point source of light $1\mathrm{m}$ away. What happens when the source is shifted to $2\mathrm{m}$?

Answer 1

Photoelectric cell:

• In a Photoelectric cell, a photosensitive cathode emits electrons when illuminated and an anode collects the emitted electrons.
• The number of photoelectrons depends on the intensity of the incident light.
• The intensity of light is inversely proportional to the square of the distance.
• So, the intensity of the light at a point, $\mathrm{I}$ is directly proportional to $\frac{1}{{\mathrm{r}}^2}$, where $\mathrm{r}$ is the distance from the source.

Finding the effect of shifting the source away:

• It is given that the source is shifted from $1m$ to $2\mathrm{m}$.
• So, $r_1=1m$and $r_2=2m$

As we know that,

$\frac{{\mathrm{I}}_2}{{\mathrm{I}}_1}=\frac{{\mathrm{r}}_1^2}{{\mathrm{r}}_2^2}$

$\Rightarrow$ $\frac{{\mathrm{I}}_2}{{\mathrm{I}}_1}=\frac{{\left(1\right)}^2}{{\left(2\right)}^2}$

$\Rightarrow$ $\frac{{\mathrm{I}}_2}{{\mathrm{I}}_1}=\frac{1}{4}$

$\Rightarrow$ ${\mathrm{I}}_2=\frac{1}{4}{\mathrm{I}}_1$

Hence, when the source is shifted to $2\mathrm{m}$ then the number of electrons emitted is a quarter of the initial number.