Question

The energy of light photons varies with wavelength. Calculate the energy per mole of photons for each of the given colors of visible light. red light, i = 721 nm E = green light, i = 535 nm E = mol blue light, = 407 nm E = Splitting liquid water into hydrogen and oxygen requires an input of 286 kJ/mol. 286 kJ + H2O(l) — H,(g) + 0,(g) Assuming a mechanism existed in which one photon of light could split one molecule of water, which color of visible light has enough energy to carry out this reaction? green Oblue o red

Answer 1

nepergy of one photon is given by E. = be (h Plank's const. X ( speed of lig hc = 19.86 x 10-26 (Numerically for I mol Photons NA = 6.022 x 1023 Photon Avogadro's no. E= NE = Na be (Energy per) ta Red Tight - x = 721 nm 7-21 x 10th - Eo = 19,86 X 10^6 = 2.75X10-19 J E = NA Eo = 6.022 X 2.758 10 23 x 10 19 = 1.656 X 10J /mol = 165.6 kJ/mol Green light - A=5.35x107 m. mol 7. 218 10-7 E 19.86810-26 5.35 x 10-7 = 3.7 870-197 E-NAE = 6.022x10 23x3.71810-19 - 22 3.41 kJ/mol Blue light - 1=4.078 107 m I - 19.86x10-26 = 488X10-19 J E = No Eo 6.022x1023x 4.888 10-19 - 293.87 kJ/mol to = 4.078 10-t

To split one H₂O molecule energy required (.x 286 X 103 - 6.022 X 1023 x = 4.75X10 It H₂o is to be broken by one Photon then energy of one photon (Eo ) х This is possible only for Blue light.