Q. Energy from the sun is received on earth at the rate of 2 cal per ${cm}^{2}$ per min. if average wavelength of solar light be taken at 5500 A then how many photons are received on the earth per ${cm}^{2}$ per min? (Take $h = 6.6 \times 10^{- 34}$Js, 1cal=4.2 J).
A) $1.5 \times 10^{13}$
B) $2.9 \times 10^{13}$
C) $2.3 \times 10^{19}$
D) $1.75 \times 10^{19}$
Explanation
(c) Energy received from the sun
$= 2\ {cal\ cm}^{- 2}{(min)}^{- 1}$
=$8.4\ J\ {cm}^{- 2}\ ({min)}^{- 1}$
Energy of 1 photon received from the sun
$E = \frac{hc}{\lambda}$
= $\frac{6.6 \times 10^{- 34} \times 3 \times 10^{8}}{5500 \times 10^{- 10}}$
=3.6$\times 10^{- 19}$ J
$\therefore$ Number of photons reaching the earth per ${cm}^{2}$per minute will be
$n = \frac{energy\ received\ from\ sun\ }{energy\ of\ one\ photon\ }$
$n = \frac{8.4}{3.6 \times 10^{- 19}} = 2.3 \times 10^{19}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.