Estimate the number of photons emitted by the Sun in a year. (Take the average wavelength to be 550 nm and the intensity of sunlight reaching the Earth (outer atmosphere) as 1350W/m2.)

We get the number of photons by dividing the amount of sun-emitted total energy by the energy per photon.

The energy of a photon of wavelength λλ is: Eλ=hc/λEλ=hc/λ where hh is Planck's Constant and cc is the speed of light.

Following the class in the video description, we assume λ=700nm=7.0×10−7mλ=700nm=7.0×10−7m for the wavelength of some sort of "average" photon from the sun.

The energy of a 700nm700nm photon is (see (b) above): E700nm=(6.3×10−34Js)×(3.0×108m/s)7.0×10−7m=2.7×10−19JE700nm=(6.3×10−34Js)×(3.0×108m/s)7.0×10−7m=2.7×10−19J.

Then the rate of photon emission by the sun is:

Nsun,out≈2.8×1026J/s2.7×10−19J≈1×1045Nsun,out≈2.8×1026J/s2.7×10−19J≈1×1045 photons/s/s.