A 10 W source gives monochromatic light of wavelength 300 nm. Placed 1 m away from a photosensitive metal surface, it releases photoelectrons. The source is now moved to 0.5 m from the surface. The intensity of light at the surface varies as the inverse square of the distance. The number of photoelectrons emitted per second is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → increased by a factor of 4
The 300 nm light already releases photoelectrons. Moving the source does not change its frequency, so only the intensity at the surface changes. For a frequency above threshold, the number of photoelectrons emitted per second is directly proportional to the intensity of the incident light. Here the intensity varies as \( 1/r^{2} \).
\( \begin{aligned} \frac{I_2}{I_1} &= \frac{r_1^{2}}{r_2^{2}} \\ &= \frac{(1\,\mathrm{m})^{2}}{(0.5\,\mathrm{m})^{2}} \\ &= 4 \end{aligned} \)
Therefore, the number of photoelectrons emitted per second also becomes 4 times. Their maximum kinetic energy stays the same.
NCERT (2026-27):
Effect of Intensity of Light on Photocurrent – “… 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.”