Assuming the sun is directly overhead, the surface of the earth receives sunlight at 1.4 10^3 W m ⁻² . Treat the light as monochromatic with an average wavelength of 500 nm , and assume no light is absorbed between the sun and the earth's surface. The distance from the sun to the earth is 1.5 10¹¹ m . Determine the number of photons the sun emits per second.

Step-by-step solution

Intensity of sunlight at the earth's surface, I = 1.4 10^3 W m ⁻² Distance from the sun to the earth, R = 1.5 10¹¹ m Total power emitted by the sun, P = I 4 R^2 P = 1.4 10^3 4 3.14 (1.5 10¹¹)^2 = 3.96 10²⁶ W Energy of a single photon, E = hc E = 6.63 10⁻³⁴ 3 10^8 500 10⁻⁹ = 3.98 10⁻¹⁹ J Number of photons emitted per second, N = P E N = 3.96 10²⁶ 3.98 10⁻¹⁹ 9.9 10⁴⁴