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

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•1900 +/- 10.•The end of physics•Tricky bits

•Motion of the earth with respect to “ether”•(Einsteinian relativity)

•Black body radiation•(Quantum mechanics)

Black Body radiation

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Radiation given off by hot stuff

Black Body radiation

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The problem

fig 27-5

Black Body radiation

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Planck’s solution

Planck proposes a quantum hypothesisEmin = hf

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

E = nhf, n = 1,2,3,...Hypothesis fits data exactly.Planck thinks it’s just math, not reality

Einstein’s photon theory

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Einstein:Reality is quantumRadiation is also quantizedPhotons = corpuscular theory

E = hf v = fE = Photon energy (Joules)v = c = speed of light = 3.00 x 108 m/sf = frequency (Hz) = wavelength (m)

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E = hf v = fE = Photon energy (Joules)v = c = speed of light = 3.00 x 108 m/sf = frequency (Hz) = wavelength (m)

Example 1: What is the energy of a 460 nm photon?v = f, c = f, f = c/E = hf = hc/

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E = hf v = fE = Photon energy (Joules)v = c = speed of light = 3.00 x 108 m/sf = 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/fE = hf, f = E/h = c/f = hc/E

Whiteboards: Photons

1 | 2 | 3 | 4

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4.36 x 10-19 J W

E = hf = (6.626 x 10-34 Js)(6.58 x 1014 s-1) = 4.36 x 10-19 J

What is the energy of a photon with a frequency of 6.58 x 1014 Hz?

8.23 x 1015 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 1015 Hzv = f, = v/f = (3.00 x 108 m/s)/(8.23 x 1015 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?

6.33 x 10-19 J, 3.95 eV W

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

What is the energy in Joules of a 314 nm photon? What is that energy in eV? (2)

206 nm W

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 W

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)

Waves Photons

Color

Brightness

Energy per photon changesE = hfX-Rays, UV, Gamma

Wavelength Changes

Amplitude Changes # of photons changesmany = brightfew = dimCCD Devices, High speed film

big = red

small = blue

small = dim

big = bright

Light