Question

The energy flux of sunlight reaching the surface of the earth is $1.388 \times 10^{3} Wm ^{-2}$. Assuming the sunlight average wavelength as $550 nm$, how many photons (nearly) per square metre are incident on the earth per second.

• A. $2 \times 10^{21}$ photons $m ^{-2} s ^{-1}$
• B. $3 \times 10^{21}$ photons $m ^{-2} s ^{-1}$
• C. $4 \times 10^{21}$ photons $m ^{-2} s ^{-1}$
• D. $5 \times 10^{21}$ photons $m ^{-2} s ^{-1}$

Answer 1

Answer: (C)

$E_{\text {photon }}=\frac{h c}{\lambda}=\frac{1242 eV - nm }{550 nm }=2.26\, eV$
$P=N E ; \frac{N}{A}=\left(\frac{P}{A}\right) \frac{1}{E}$
Photons per second per unit area
$=\frac{1.388 \times 10^{3} W / m ^{2}}{\left(2.26 \times 1.6 \times 10^{-19} J \right)}=3.8 \times 10^{21}$
$\approx 4 \times 10^{21}$ photons $m ^{-2} s ^{-1}$