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 10 8 m/s f = frequency (Hz) = wavelength (m)

2. E = hf, h = 6.626E-34 Js v = f E = Photon energy (Joules) v = c = 3.00 x 10 8 m/s f = frequency (Hz) = wavelength (m) Example 1: What is the energy of a 460. nm photon? 4.3213E-19 J, 2.70 eV

3. E = hf v = f E = Photon energy (Joules) v = c = 3.00 x 10 8 m/s f = frequency (Hz) = wavelength (m) 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

4. 4.36 x 10 -19 J E = hf = (6.626 x 10 -34 Js)(6.58 x 10 14 s -1 ) = 4.36 x 10 -19 J Ex1 What is the energy (in J) of a photon with a frequency of 6.58 x 10 14 Hz?

5. 36.5 nm 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) = 3.65E-8 m = 36.5 nm Ex2 - What is the wavelength of a photon with an energy of 5.45 x 10 -18 J?

6. 6.33 x 10 -19 J, 3.95 eV 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)/(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 Ex3 -What is the energy (in eV) of a 314 nm photon?

7. 206 nm 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)

8. 9.36 x 10 17 photons/sec 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)