From the wave equation, v = fλ. This relates the wave speed (v), the frequency (f) and the wavelength (λ). We know that in air, the speed of electromagnetic radiation is very close to the speed of electromagnetic radiation in a vacuum, since the refractive index of air is very close to 1. Therefore we can replace v with c, the speed of light in a vacuum.

Now we have c = fλ. Rearranging, this gives f = c/λ.

Next from quantum theory, we are given that E = hf. This relates the energy of a photon, or particle of light, (E), and the frequency of the light (f), with the constant of proportionality ‘Planck’s Constant’ (h).

Combining this with the wave equation, we arrive at E = hc/λ.

Plugging in h = 6.6*10^-34Js^-1, c = 3.0*10^8ms^-1 and λ = 5.0m (all to two significant figures):

E = (6.6*10^-34)(3.0*10^8)/(5.0) = 4.0*10^26J per photon. I hope this helps you 🙂