We can find the energy of a photon, given frequency, with this equation:
E = h nu, where E is the energy of the photon in J, h is Planck's constant of 6.626*10^-34 Js, and nu is the frequency in "Hz".
The problem gives us wavelength instead of frequency, but we can actually solve this problem by combining E = h nu with another equation:
c = lambda nu, where c is the speed of light at 3.0*10^8 "m/s" and lambda is the wavelength in m
After combining them, we'll be able to find the energy of a photon given wavelength.
c = lambda nu
nu = c/lambda
E = h nu
E = hc/lambda
Now, before we plug in the wavelength of 555nm, we need to convert 555nm into m, which would be 5.55*10^-7m.
E = hc/lambda
E = 6.626*10^-34 Js xx (3.0*10^8 m"/"s)/(5.55*10^-7m)
E = 6.626*10^-34 Jcancel(s) xx (3.0*10^8 cancel(m)"/"cancel(s))/(5.55*10^-7cancel(m))
E = 3.58 * 10^-19 J
This is the amount of energy for 1 photon. However, we want it for 1 mole of photons, which means that there's 6.022*10^23 photons.
E = 3.58 * 10^-19 J xx 6.022*10^23 = "216000J/mol"
After converting it into kJ, this would be "216 kJ/mol".