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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.
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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 nm
= 550 × 10−9 m
Number of photons per square metre incident on earth per second = n
Hence, the equation for power can be written as:
P = nE
∴ n = `"P"/"E" = ("P"lambda)/"hc"`
= `(1.388 xx 10^3 xx 550 xx 10^(-9))/(6.626 xx 10^(-34) xx 3 xx 10^8)`
= 3.84 × 1021 photons/m2/s
Therefore, every second, 3.84 × 1021 photons are incident per square metre on earth.
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