The relationship between energy of a single photon and its wavelength can be determined using the formula E=hc/lambda where h is Planck's constant, c is the speed of light, and lambda is the wavelength in units of meters. If we can find the energy of a single wavelength of 565 nm, we can then determine the number of photons that total 0.861 J.
Before we can solve for the energy, we need to convert 565 nm to meters.
565 nm (1 m / 1 x 10^9 nm) = 5.65 x 10^-7 m
Then, we can plug in the values we know into the equation
E = (6.63 x 10^-34 Js)(3 x 10^8 m/s) / 5.65 x 10^-7 m
E = 3.52 x 10^-19 J
This gives us the energy in Joules of a single photon. Now, we can find the number of photons in 0.861 J
0.861 J / 3.52 x 10^-19 J = 2.45 x 10^18 photons