Final answer:
The energy of a mole of red photons of wavelength 725 nm is 2.74 x 10^(-19) J.
Step-by-step explanation:
The energy of a photon can be calculated using the equation E = hf, where E is the energy, h is Planck's constant (6.626 x 10-34 J-s), and f is the frequency of the photon. Since the question provides the wavelength of the red photon (725 nm), we need to convert it to frequency by using the equation c = λf, where c is the speed of light (3.00 x 108 m/s). Rearranging the equation to solve for f, we get f = c/λ. Substituting the values, we have f = (3.00 x 108 m/s) / (725 x 10-9 m) = 4.14 x 1014 Hz. Using this value for f, we can now calculate the energy by multiplying it with Planck's constant, giving us: E = (6.626 x 10-34 J-s) x (4.14 x 1014 Hz) = 2.74 x 10-19 J.