Question

Photoelectric cell is illuminated by a small intense source distant 1 m from it. When the same source is placed at a distance 2 m then the number of photoelectrons emitted from the cathode will be

• A. Half
• B. One fourth
• C. Each carries one fourth of its previous energy
• D. Each carries one fourth of its previous momentum

Answer 1

Answer: (B)

One fourth

Let, the distance of source are $r_1=1m$ and $r_2=2m$
The intensity o incident light is given by is given by

$I=\frac{P}{4\pi r^2}$

$\Rightarrow I\propto \frac{1}{r^2}$

The photocurrent is directly proportional to the intensity of incident light.
Also, number of photoelectrons emitted (say)n are directly proportional to the photocurrent.
Hence,
$n\propto I\propto \frac{1}{r^2}$

$\Rightarrow n_1\propto \frac{1}{r_1^2}$ and $n_2\propto \frac{1}{r_2^2}$

$\Rightarrow \frac{n_2}{n_1}=\frac{r_1^2}{r_2^2}$

$\therefore n_2=\frac{1}{2^2}{n}_1$

$\therefore n_2=\frac{1}{4}{n}_1$

Hence, if the distance of source increases twice the number of photoelectrons emitted will become one fourth.

So, the answer is option (B).