Energy of a Photon Calculate the energy of one photon of yellow light that has a wavelength of 589 nm. (a) A laser emits light that has a frequency of 4.69 * 1014 s-1. What is the energy of one photon of this radiation? (b) If the laser emits a pulse containing 5.0 x 1017 photons of this radiation, what is the total energy of that pulse? (c) If the laser emits 1.3* 10-2 J of energy during a pulse, how many photons are emitted?

Solution: 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/ , where, is the wavelength of light and c is the velocity. Step1: 14 -1 a) Given, frequency of the light = 4.69 x 10 s Planck's constant, h = 6.626 x 10 J.s -34 Substituting the values in equation (1), we get, -34 14 -1 E = (6.626 x 10 J.s) x (4.69 x 10 s ) = 31.076 x 10 J -20 = 3.1076 x 10 J. -19 -19 Thus, energy of one photon of the radiation is 3.1076 x 10 J. Step2: 17 b) Number of photons emitted = 5.0 x 10 . Energy of one photon = 3.1076 x 10 J. -19 Therefore, total energy of 5.0 x 10 photons = (5.0 x 10 ) x (3.1076 x 10 J) -19 -2 = 15.538 x 10 J = 0.155 J. Step3: c) Given, total energy of the photons = 1.3 x 10 J -2 Energy of one photon = 3.1076 x 10 J. -19 -2 -19 Therefore, number of photons emitted = (1.3 x 10 J) / (3.1076 x 10 J) = 0.42 x 10 . 17 = 4.2 x 10 . 16 16 Thus, 4.2 x 10 photons are emitted. --------------