Question

The energy flux of sunlight reaching the surface of the earth is $1.52 \times 10^{3} \,Wm ^{-2}$. The photons in the sunlight have an average wavelength of $520\, nm$. How many photons per square metre are incident on the earth per second?

• A. $4 \times 10^{21}$
• B. $4 \times 10^{34}$
• C. $4 \times 10^{31}$
• D. $4 \times 10^{28}$

Answer 1

Answer: (A)

Here, $I=1.52 \times 10^{3} \,Wm ^{-2}$
$\lambda=520 \times 10^{-9} \,m$
$ \Rightarrow h=6.63 \times 10^{-34}\, Js$
Number of photons incident on earth's surface per second per square metre is
$n=\frac{I}{E}=\frac{I}{h c} \lambda \left[\because E=\frac{h c}{\lambda}\right]$
$n=\frac{1.52 \times 10^{3} \times 520 \times 10^{-9}}{6.63 \times 10^{-34} \times 3 \times 10^{8}}$
$=4 \times 10^{21}$ Photons per $m ^{2}$ per second