Question

A $5$ watt source emits monochromatic light of wavelength $5000\,\mathring{A}$. When placed $0.5\, m$ away, it liberates photoelectrons from a photosensitive metallic surface. When the source is moved to a distance of $1.0 \,m$, 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 $P _{0}=5 W$
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 : $r_{1}=0.5 \,m \,\,\,\, r_{2}=1 m$
$\frac{ N _{2}}{ N _{1}}=\frac{0.5^{2}}{1^{2}}=\frac{1}{4}$