To calculate how many photons are in a certain amount of energy (joules) we need to know how much energy is in one photon.
Start by using two equations:
Energy of a photon = Frequency Planck's constant (6.626 10^(-34) J-s)
Speed of light (constant 3 10^8 m/s) = Frequency Wavelength
Which means:
frequency = Speed of Light / Wavelength
So energy of a photon = (Speed of light Planck's constant)/(Wavelength)
You may have seen this equation as E = hc/λ
We have a wavelength of 691 nm or 691 10^-9 meters
So we can plug in all of our knowns:
E = (6.626 10^(-34) J-s) (3.00 10^8 m/s) / (691 10^-9 m) =
2.88 10^(-19) joules per photon
Now we have joules per photon, and the total number of joules (0.862 joules)
,so divide joules by joules per photon, and we have the number of photons:
0.862 J/ (2.88 10^(-19) J/photon) = 3.00 * 10^18 photons.
