Question

A $5$ watt source emits monochromatic light of wavelength $5000\mathring{A}$. 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 photo electrons liberated will:

• A. be reduced by a factor of 8
• B. be reduced by a factor of 16
• C. be reduced by a factor of 2
• D. be reduced by a factor of 4

Answer 1

Answer: (D)

Power of the source $P_0=5W$
Power at the distance $r$ from source, $P=\frac{P_{\circ }}{4\pi r^2}$....(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 $N\propto \frac{1}{r^2}$
$\Rightarrow \frac{N_2}{N_1}=\frac{r_1^2}{r_2^2}$
Given : $r_1=0.5m{r}_2=1m$
$\frac{N_2}{N_1}=\frac{0.5^2}{1^2}=\frac{1}{4}$