How many photons are produced in a laser pulse of 0.862 J at 691 nm?

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.