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 2
Whiteboards
                               
                                           

2. Black Body radiation Radiation given off by hot stuff TOC
What BBR is – demo
Note peak – hotter is bluer
The end of physics
Planck’s problem
The solution
Steps vs. ramp
Vibrations are “auto tuned”
TOC

3. Einstein’s photon theory
Einstein: (Quantum jump)
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 108 m/s
f = frequency (Hz)
 = wavelength (m)
Ex. 1: Energy of a 460 nm photon?
Ex. 2: Wavelength of a 13.6 eV photon?
TOC

4. E = Photon energy (Joules) v = c = speed of light = 3.00 x 108 m/s
E = hf
v = f
E = Photon energy (Joules)
v = c = speed of light = 3.00 x 108 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/ = (6.626E-34 Js)(3.00E8 m/s)/(460E-9m) =
4.3213E-19 J = (4.3213E-19 J)/(1.602E-19 J/eV) = 2.70 eV
TOC

5. E = Photon energy (Joules) v = c = speed of light = 3.00 x 108 m/s
E = hf
v = f
E = Photon energy (Joules)
v = c = speed of light = 3.00 x 108 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 (in Joules) = (13.6 eV)(1.602 x J/eV) = E-18 J
c = f,  = c/f
E = hf, f = E/h
 = c/f = hc/E = (6.626E-34 Js)(3.00E8 m/s)/( E-18 J) =
E-08 m = 91.2 nm (1 nm = 1x10-9 m)
TOC

6. Whiteboards:
Photons
1 | 2 | 3 | 4
TOC

7. What is the energy (in J) of a photon with a frequency of 6
What is the energy (in J) of a photon with a frequency of 6.58 x 1014 Hz?
E = hf
= (6.626 x Js)(6.58 x 1014 s-1) = 4.36 x J W
4.36 x J

8. What is the wavelength of a photon with an energy of 5.45 x 10-18 J?
E = hf
f = E/h = (5.45 x J)/(6.626 x Js)
= 8.23 x 1015 Hz
v = f,  = v/f = (3.00 x 108 m/s)/(8.23 x 1015 Hz)
= 3.65E-8 m = 36.5 nm W
36.5 nm

9. What is the energy (in eV) of a 314 nm photon? (2)
E = hf = hc/
1eV = x J
E = hc/
= (6.626 x Js)(3.00 x 108 m/s)/(314 x 10-9 m) = 6.33 x J
E = (6.33 x J)/(1.602 x J/eV) = 3.95 eV W
6.33 x J, eV

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

11. How many photons per second stream from a 620. nm, 300. mW laser? (2)
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 108 m/s)/(620. x 10-9 m)
= x J (per photon)
# photons = (.300 J/s)/( x J/photon)
= 9.36 x 1017 photons/sec
Hey, that’s a lot! W
9.36 x 1017 photons/sec

12. Light
Waves Photons
Wavelength Changes
Energy per photon changes
E = hf
Radio Waves vs. X-rays
Color
small  = blue
big  = red
Amplitude Changes
# of photons changes
many = bright
few = dim
CCD Devices, High speed film
small = dim
Brightness
big = bright