Question

At noon on a clear day, sunlight reaches the earth\'s surface at Madison, Wisconsin, with an average intensity of approximately 2.00 kJ·s–1·m–2. If the sunlight consists of photons with an average wavelength of 510.0 nm, how many photons strike a 4.80 cm2 area per second?

Answer 1

I = average intensity of sunlight reaching at Madison = 2000 Js⁻¹m⁻²

A = area on which the light strike = 4.80 cm² = 4.80 x 10⁻⁴ m²

energy received per second by the area is given as

E = IA

inserting the values

E = (2000) (4.80 x 10⁻⁴)

E = 0.96 J

λ = wavelength of the photons in the sunlight = 510 x 10⁻⁹ m

c = speed of light = 3 x 10⁸ m/s

h = plank's constant = 6.63 x 10⁻³⁴ J-s

n = number of photons received per second

energy received per second is also given as

E = n h c /λ

inserting the values

0.96 = n (6.63 x 10⁻³⁴) (3 x 10⁸) /(510 x 10⁻⁹)

n = 2.5 x 10¹⁸ per second