Question

Solar radiation still has an intensity of 1367 watts per square meter at the top of Earths atmosphere, and Earth has a radius of 6370 km. How many photons hit Earth per second? You may assume that all of the photons are at the sun’s peak wavelength, 500 nm.

Answer 1

We know intensity = energy / area

Therefore surface area of earth = 4 * pi * r² = 4 * pi * 6370000² = 5.09 * 10¹⁴ m²

thus Energy = intensity * area = 1367 * 5.09 * 10¹⁴ = 6.96 * 10¹⁷ Joule

now we also have energy of one photon = h c / lambda = 6.63 *10^-34 *3 *10⁸ / 500 *10^-9 = 3.978*10^-19J

where c is speed of light and h is planck’s constant. 1nm = 10^-9m

Therefore number of photon = total energy / energy of one photon = 6.96*10¹⁷/3.978*10^-19= 1.749*10^{36 [Answer]}