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.

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Einstein’s photon theory Photons = corpuscular theory E = hf E = Photon energy (Joules) h = Planck’s constant = x 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)

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? E-19 J, 2.70 eV

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) E-08 m = 91.2 nm

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

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

6.33 x J, 3.95 eV E = hf = hc/ 1eV = x J E = hc/ = (6.626 x Js)(3.00 x 10 8 m/s)/(314 x m) = 6.33 x J E = (6.33 x J)/(1.602 x J/eV) = 3.95 eV Ex3 -What is the energy (in eV) of a 314 nm photon?

206 nm E = hf = hc/ 1eV = x J E = (6.02 eV)(1.602 x J/eV) = 9.64 x J E = hc/, = hc/E = (6.626 x Js)(3.00 x 10 8 m/s)/(9.64 x J) = 2.06 x m = 206 nm (nm = 1 x m) A photon has an energy of 6.02 eV. What is its wavelength? (answer in nm) (2)

9.36 x 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 Js)(3.00 x 10 8 m/s)/(620. x m) = x J (per photon) # photons = (.300 J/s)/( x J/photon) = 9.36 x photons/sec Hey, that’s a lot! How many photons per second stream from a 620. nm, 300. mW laser? (2)