A photo cathode is illuminated by a very small bright source placed 1 m away. When the same source of light is placed 0.5 m away, the number of electrons emitted by the photo cathode would become
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → four times
In the photoelectric effect the number of photoelectrons emitted per second is proportional to the intensity of the light. A very small source behaves as a point source, whose intensity falls as the inverse square of the distance.
\( \displaystyle I = \frac{P}{4\pi r^{2}} \;\Rightarrow\; I \propto \frac{1}{r^{2}} \)
\( \displaystyle \frac{I_2}{I_1} = \left(\frac{r_1}{r_2}\right)^{2} = \left(\frac{1}{0.5}\right)^{2} = 4 \)
The intensity becomes four times, so the number of emitted electrons also becomes four times. The frequency is unchanged, so the energy of each photoelectron stays the same.
NCERT (2026-27):
Effect of Intensity of Light on Photocurrent – “… It is found that the photocurrent increases linearly with intensity of incident light as shown graphically in Fig. 11.2. The photocurrent is directly proportional to the number of photoelectrons emitted per second. This implies that the number of photoelectrons emitted per second is directly proportional to the intensity of incident radiation.”