The energy flux of sunlight reaching the surface of the earth is
Question:

The energy flux of sunlight reaching the surface of the earth is 1.388 × 103 W/m2. How many photons (nearly) per square metre are incident on the Earth per second? Assume that the photons in the sunlight have an average wavelength of 550 nm.

Solution:

Energy flux of sunlight reaching the surface of earth, Φ = 1.388 × 103 W/m2

Hence, power of sunlight per square metre, P = 1.388 × 103 W

Speed of light, c = 3 × 108 m/s

Planck’s constant, h = 6.626 × 10−34 Js

Average wavelength of photons present in sunlight, $\lambda=550 \mathrm{~nm}$

$=550 \times 10^{-9} \mathrm{~m}$

Number of photons per square metre incident on earth per second = n

 

Hence, the equation for power can be written as:

$P=n E$

$\therefore n=\frac{P}{E}=\frac{P \lambda}{h c}$

$=\frac{1.388 \times 10^{3} \times 550 \times 10^{-9}}{6.626 \times 10^{-34} \times 3 \times 10^{8}}=3.84 \times 10^{21}$ photons $/ \mathrm{m}^{2} / \mathrm{s}$

Therefore, every second, $3.84 \times 10^{21}$ photons are incident per square metre on earth.

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