First, we need to calculate the energy of a single photon of this radiation.
The wavelength of the photons is:
[tex]\lambda=560 nm = 5.6 \cdot 10^{-7}m [/tex]
And their frequency is:
[tex]f= \frac{c}{\lambda}= \frac{3 \cdot 10^8 m/s}{5.6 \cdot 10^{-7} m}=5.36 \cdot 10^{14}Hz [/tex]
So the energy of one photon is
[tex]E_1=hf=(6.6 \cdot 10^{-34}Js)(5.36 \cdot 10^{14} Hz)=3.54 \cdot 10^{-19} J[/tex]
The intensity of the solar radiation on Earth's surface is [tex]1900 W/m^2[/tex]. This means that the power is P=1900 W. But the power is just the energy per second:
[tex]P= \frac{E}{t} [/tex]
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:
[tex]N= \frac{E}{E_1}= \frac{1900 J}{3.54 \cdot 10^{-19} J}=5.37 \cdot 10^{21}ph \cdot m^2 /s[/tex]
