Question

A $160\, W$ infrared source is radiating light of wavelength $50000 \, \mathring{A}$ uniformly in all directions. The photon flux at a distance of $1.8\, m$ is the order of

• A. $10\, m^{-2}s^{-1}$
• B. $10^{10} m^{-2}s^{-1}$
• C. $10^{15} m^{-2}s^{-1}$
• D. $10^{20} m^{-2}s^{-1}$

Answer 1

Answer: (D)

Total photons emitted from source is

$N=\frac{\text { Power }}{h c / \lambda}=\frac{160 \times 50000 \times 10^{-10}}{6.6 \times 10^{-34} \times 3 \times 10^{8}}$
So, photon flux falling over spherical surface of radius $r=18\,m$ is
$n =\frac{N}{A}=\frac{N}{4 \pi r^{2}}$
$=\frac{160 \times 50000 \times 10^{-6}}{6.6 \times 10^{-34} \times 3 \times 10^{8} \times 4 \pi \times(1.8)^{2}}$
$\approx 10^{20} m ^{-2} s ^{-1}$