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.
Energy of a photon E = hv = hc / λ
Where h = plank’s constant = 6.63 × 10-34 J. sec
ν = average frequency of sunlight
c = speed of light = 3 × 108 m/s
λ = average wavelength of sunlight
E = 6.63 × 10-34 × 3 × 108 / 550 × 10-9 = 3.61 × 10-19 J
ϕ = energy flux per unit area (sq. meter) per sec. falling on the earth.
n = let no. of photons falling per sec. per sq. meter on earth surface.
ϕ = n × E
n = ϕ/E
n = 1.388 × 103/3.61 × 10-19 = 3.85 × 1021 photons/m2.sec
no. of photons falling on Earth surface per square meter per sec. is 3.85 × 1021 photons/m2.sec.