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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.
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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