Problem 30E

What are the main sources of the energy consumed in the United States?

Solution: Step1: Given, the energy required to break the Cl-Cl bond in Cl = 242 kJ/mol 2 = 242 x 10 J/mol 3 23 = (242 x 10 J) / (6.023 x 10 ) [1 mol = 6.023 x 10 photons] = 40.18 x 10 -20J -19 = 4.02 x 10 J. Step2: According to Planck’s quantum theory of radiation, the amount of energy associated with a quantum(in case of light, the quantum of energy is often called photon) of radiation is proportional to the frequency of light, E = h ---(1), where h is a universal constant called Planck’s constant. is the frequency and E is the energy of a photon. Or, E = hc/ -------(2), where, is the wavelength of light and c is the velocity. -19 Here, energy of the radiation emitted = 4.02 x 10 J. -34 Planck's constant, h = 6.626 x 10 J.s Velocity of light, c = 3 x 10 m/sec 8 Substituting the values in equation (2), we get, 4.02 x 10 -19J = [(6.626 x 10 J.s) x (3 x 10 m/sec)] / = [(6.626 x 10 J.s) x (3 x 10 m/sec)] / (4.02 x 10 -19J) -7 = 4.94 x 10 m. Thus, the longest wavelength of radiation that possesses the necessary energy to break the bond -7 is 4.94 x 10 m. Step3: Out of all the radiations in the electromagnetic spectrum, the wavelength of the visible light ranges from 4 x 10 m to 7 x 10 m. Thus, the electromagnetic radiation in the above problem lies in the visible light region. --------------------