Question

The energy of light photons varies with wavelength. Calculate the energy per mole of photons for each of the following colors of visible light. Red Light, ? = 691 nm Green Light, ? = 527 nm Blue Light, ? = 411 nm

Answer 1

Part 1)

Red light, = 691 nm

Frequency, v = c/ = (3 x 108 m/s)/(691 x 10-9 m ) = 4.341 x 10¹⁴/s

Energy, E = hv = (6.626 x 10^-34 J s) x (4.341 x 10¹⁴ /s) = 2.876 x 10^-19 J

Energy per mol = (2.84 x10^-19 J) x (6.023 x 10²³ photons/mol) = 1.732 x 10⁵ J/mol = 1.732 x 10² kJ/mol

Energy of red light = 1.73 x 10² kJ/mol

Part 2)

Green Light, = 527 nm

Frequency, v = c/ = (3 x 10⁸ m/s)/(527 x 10^-9 m ) = 5.692 x 10¹⁴/s

Energy, E = hv = (6.626 x 10^-34 J s) x (5.692 x 10¹⁴/s) = 3.771 x 10^-19 J

Energy per mol = (3.771 x 10^-19 J) x (6.023 x 10²³ photons/mol) = 2.271 x 10⁵ J/mol = 2.271 x 10² kJ/mol

Energy of green light = 2.27 x 10² kJ/mol

Part 3)

Blue Light, = 411 nm

Frequency, v = c/ = (3 x 10⁸ m/s)/(411 x 10^-9 m ) = 7.299 x 10¹⁴/s

Energy, E = hv = (6.626 x 10^-34 J s) x (7.299 x 10¹⁴/s) = 4.836 x 10^-19 J

Energy per mol = (4.836 x 10^-19 J) x (6.023 x 10²³ photons/mol) = 2.913 x 10⁵ J/mol = 2.913 x 10² kJ/mol

Energy of blue light = 2.91 x 10² kJ/mol