Question

A 5 watt source emits monochromatic light of wavelength 5000. When placed 0.5m away, it liberates photoelectrons from a photosensitive metallic surface. When the source is moved to a distance of 1.0m, the number of photoelectrons liberated will be reduced by a factor of

• A. 8
• B. 16
• C. 2
• D. 4

Answer 1

The correct option is D 4

Power of the source $P_o=5W$
Power at the distance $r$ from source, $P=\frac{P_o}{4\pi r^2}$ .....(1)
Each photon emits one electrons.
Also, $P\propto N$ .....(2)
$N$ is the number of photons (or photo electrons).
From (1) and (2) we get, number of photo electrons $N\propto \frac{1}{r^2}$
$⟹$ $\frac{N_2}{N_1}=\frac{r_1^2}{r_2^2}$
Given : $r_1=0.5m$ $r_2=1m$
$\frac{N_2}{N_1}=\frac{{0.5}^2}{1^2}=\frac{1}{4}$