Einstein’s photon theoryPhotons = corpuscular theory

E = hf E = Photon energy (Joules) h = Planck’s constant = 6.626 x 10-34 Jsf = frequency of oscillations (Hz, s-1)

v = fv = c = speed of light = 3.00 x 108 m/sf = frequency (Hz) = wavelength (m)

E = hf, h = 6.626E-34 Jsv = fE = Photon energy (Joules)v = c = 3.00 x 108 m/sf = frequency (Hz) = wavelength (m)

Example 1: What is the energy of a 460. nm photon? 4.3213E-19 J, 2.70 eV

E = hf v = fE = Photon energy (Joules)v = c = 3.00 x 108 m/sf = 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

4.36 x 10-19 J

E = hf = (6.626 x 10-34 Js)(6.58 x 1014 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 1014 Hz?

36.5 nm

E = hf f = E/h = (5.45 x 10-18 J)/(6.626 x 10-34 Js) = 8.23 x 1015 Hzv = f, = v/f = (3.00 x 108 m/s)/(8.23 x 1015 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?

6.33 x 10-19 J, 3.95 eV

E = hf = hc/1eV = 1.602 x 10-19 JE = 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

Ex3 -What is the energy (in eV) of a 314 nm photon?

206 nm

E = hf = hc/1eV = 1.602 x 10-19 JE = (6.02 eV)(1.602 x 10-19 J/eV) = 9.64 x 10-19 JE = 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)

A photon has an energy of 6.02 eV. What is its wavelength?(answer in nm) (2)

9.36 x 1017 photons/sec

E = hf = hc/In one second, a 300 mW laser emits photons with a total energy of .300 JE = 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/secHey, that’s a lot!

How many photons per second stream from a 620. nm, 300. mW laser? (2)