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Planck’s hypothesis, and Einstein’s photon theory. Contents: Hubris at the turn of the century

Planck’s hypothesis, and Einstein’s photon theory. Contents: Hubris at the turn of the century Black Body radiation The problem with black body radiation Planck’s hypothesis Einstein’s corpuscular light theory Photons : Example 1 | Example 2 Whiteboards. Hubris. 1900 +/- 10.

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Planck’s hypothesis, and Einstein’s photon theory. Contents: Hubris at the turn of the century

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  1. Planck’s hypothesis, • and Einstein’s • photon theory. • Contents: • Hubris at the turn of the century • Black Body radiation • The problem with black body radiation • Planck’s hypothesis • Einstein’s corpuscular light theory • Photons : Example 1 | Example 2 • Whiteboards

  2. Hubris • 1900 +/- 10. • The end of physics • Tricky bits • Motion of the earth with respect to “ether” • (Einsteinian relativity) • Black body radiation • (Quantum mechanics) TOC

  3. Black Body radiation Radiation given off by hot stuff TOC

  4. Black Body radiation The problem fig 27-5 TOC

  5. Black Body radiation Planck’s solution • Planck proposes a quantum hypothesis • Emin = hf • h = Planck’s constant = 6.626 x 10-34 Js • f = frequency of oscillations (Hz, s-1) • E = nhf, n = 1,2,3,... • Hypothesis fits data exactly. • Planck thinks it’s just math, not reality TOC

  6. Einstein’s photon theory • Einstein: • Reality is quantum • Radiation is also quantized • Photons = corpuscular theory • E = hf • v = f • E = Photon energy (Joules) • v = c = speed of light = 3.00 x 108 m/s • f = frequency (Hz) •  = wavelength (m) TOC

  7. E = hf v = f E = Photon energy (Joules) v = c = speed of light = 3.00 x 108 m/s f = frequency (Hz)  = wavelength (m) Example 1: What is the energy of a 460 nm photon? v = f, c = f, f = c/ E = hf = hc/ TOC

  8. E = hf v = f E = Photon energy (Joules) v = c = speed of light = 3.00 x 108 m/s f = frequency (Hz)  = wavelength (m) Example 2: A photon has an energy of 13 eV. What is its wavelength? (Remember V = W/q, and 1 eV is one electron moved through 1 volt) E (in Joules) = (13 eV)(1.602 x 10-19 J/eV) c = f,  = c/f E = hf, f = E/h  = c/f = hc/E TOC

  9. Whiteboards: Photons 1 | 2 | 3 | 4 TOC

  10. What is the energy 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 W 4.36 x 10-19 J

  11. What is the frequency of a photon with an energy of 5.45 x 10-18 J? What is its wavelength? 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) = 36.5 nm W 8.23 x 1015 Hz, 36.5 nm

  12. What is the energy in Joules of a 314 nm photon? What is that energy in eV? (2) E = hf = hc/ 1eV = 1.602 x 10-19 J E = hc/ = (6.626 x 10-34 Js)(3.00 x 108 m/s)/(3.14 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 W 6.33 x 10-19 J, 3.95 eV

  13. 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) W 206 nm

  14. 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! W 9.36 x 1017 photons/sec

  15. small  = blue big  = red small = dim big = bright Light Waves Photons Wavelength Changes Energy per photon changes E = hf X-Rays, UV, Gamma Color Amplitude Changes # of photons changes many = bright few = dim CCD Devices, High speed film Brightness

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