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Einstein’s photon theory

Einstein’s photon theory. Photons = corpuscular theory E = hf E = Photon energy (Joules) h = Planck’s constant = 6.626 x 10 -34 Js f = frequency of oscillations (Hz, s -1 ) v = f  v = c = speed of light = 3.00 x 10 8 m/s f = frequency (Hz)  = wavelength (m).

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Einstein’s photon theory

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  1. Einstein’s photon theory • Photons = corpuscular theory • E = hf • E = Photon energy (Joules) • h = Planck’s constant = 6.626 x 10-34 Js • f = frequency of oscillations (Hz, s-1) • v = f • v = c = speed of light = 3.00 x 108 m/s • f = frequency (Hz) •  = wavelength (m)

  2. Example 1: What is the energy of a 460. nm photon? 4.3213E-19 J, 2.70 eV E = hf, h = 6.626E-34 Js v = f E = Photon energy (Joules) v = c = 3.00 x 108 m/s f = frequency (Hz)  = wavelength (m)

  3. Example 2: A photon has an energy of 13.6 eV. What is its wavelength? (Remember V = W/q, and 1 eV is one electron moved through 1 volt) 9.12371E-08 m = 91.2 nm E = hf v = f E = Photon energy (Joules) v = c = 3.00 x 108 m/s f = frequency (Hz)  = wavelength (m)

  4. Ex1 What is the energy (in J) of a photon with a frequency of 6.58 x 1014 Hz? E = hf = (6.626 x 10-34 Js)(6.58 x 1014 s-1) = 4.36 x 10-19 J 4.36 x 10-19 J

  5. Ex2 - What is the wavelength of a photon with an energy of 5.45 x 10-18 J? E = hf f = E/h = (5.45 x 10-18 J)/(6.626 x 10-34 Js) = 8.23 x 1015 Hz v = f,  = v/f = (3.00 x 108 m/s)/(8.23 x 1015 Hz) = 3.65E-8 m = 36.5 nm 36.5 nm

  6. Ex3 -What is the energy (in eV) of a 314 nm photon? E = hf = hc/ 1eV = 1.602 x 10-19 J E = hc/ = (6.626 x 10-34 Js)(3.00 x 108 m/s)/(314 x 10-9 m) = 6.33 x 10-19 J E = (6.33 x 10-19 J)/(1.602 x 10-19 J/eV) = 3.95 eV 6.33 x 10-19 J, 3.95 eV

  7. A photon has an energy of 6.02 eV. What is its wavelength? (answer in nm) (2) E = hf = hc/ 1eV = 1.602 x 10-19 J E = (6.02 eV)(1.602 x 10-19 J/eV) = 9.64 x 10-19 J E = hc/,  = hc/E = (6.626 x 10-34 Js)(3.00 x 108 m/s)/(9.64 x 10-19 J) = 2.06 x 10-7 m = 206 nm (nm = 1 x 10-9 m) 206 nm

  8. How many photons per second stream from a 620. nm, 300. mW laser? (2) E = hf = hc/ In one second, a 300 mW laser emits photons with a total energy of .300 J E = hc/, = (6.626 x 10-34 Js)(3.00 x 108 m/s)/(620. x 10-9 m) = 3.20613 x 10-19 J (per photon) # photons = (.300 J/s)/(3.20613 x 10-19 J/photon) = 9.36 x 1017 photons/sec Hey, that’s a lot! 9.36 x 1017 photons/sec

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