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 2Example Example 2 Whiteboards

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

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

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

5. Black Body radiation TOC Planck’s solution Planck proposes a quantum hypothesis E min = 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

6. Einstein’s photon theory TOC 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 10 8 m/s f = frequency (Hz) = wavelength (m)

7. TOC E = hf v = f E = Photon energy (Joules) v = c = speed of light = 3.00 x 10 8 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/

8. TOC E = hf v = f E = Photon energy (Joules) v = c = speed of light = 3.00 x 10 8 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

9. Whiteboards: Photons 11 | 2 | 3 | 4234 TOC

10. 4.36 x 10 -19 J W E = hf = (6.626 x 10 -34 Js)(6.58 x 10 14 s -1 ) = 4.36 x 10 -19 J What is the energy of a photon with a frequency of 6.58 x 10 14 Hz?

11. 8.23 x 10 15 Hz, 36.5 nm W E = hf f = E/h = (5.45 x 10 -18 J)/(6.626 x 10 -34 Js) = 8.23 x 10 15 Hz v = f, = v/f = (3.00 x 10 8 m/s)/(8.23 x 10 15 Hz) = 36.5 nm What is the frequency of a photon with an energy of 5.45 x 10 -18 J? What is its wavelength?

12. 6.33 x 10 -19 J, 3.95 eV W E = hf = hc/ 1eV = 1.602 x 10 -19 J E = hc/ = (6.626 x 10 -34 Js)(3.00 x 10 8 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 What is the energy in Joules of a 314 nm photon? What is that energy in eV? (2)

13. 206 nm W 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 10 8 m/s)/(9.64 x 10 -19 J) = 2.06 x 10 -7 m = 206 nm (nm = 1 x 10 -9 m) A photon has an energy of 6.02 eV. What is its wavelength? (answer in nm) (2)

14. 9.36 x 10 17 photons/sec W 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 10 8 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 10 17 photons/sec Hey, that’s a lot! How many photons per second stream from a 620. nm, 300. mW laser? (2)

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