Solar radiation falls on earth's surface at a rate of 1900 w/m2 . assuming that the radiation has an average wavelength of 560 nm, how many photons per square meter per second fall on the surfaces? the speed of light is 3 × 108 m/s and planck's constant is 6.62607 × 10−34 j · s. answer in units of photon/m2 · s.

First, we need to calculate the energy of a single photon of this radiation.

The wavelength of the photons is:

And their frequency is:

So the energy of one photon is


The intensity of the solar radiation on Earth's surface is . This means that the power is P=1900 W. But the power is just the energy per second:

So this means that the energy of the solar radiation per meter squared per second is E=1900 J. If we divide this number by the energy of a single photon, we find the number of photons per meter squared per second: