1. Chapter 2: Particle Properties of Waves
Electromagnetic Waves
coupled Electric and Magnetic Oscillations
harmonic waves a.k.a. sine waves Ey Bz x

2. electromagnetic spectrum l = c/f
f (Hz)
100
105
1010
1015
1020
1025
10-5
10-10
10-15
Radio
microwave
millimeter
infrared
visible
ultraviolet
x-ray
Gamma
l (m)
4.3 x x1014 (Hz)
Visible Light
ROYGBIV
700 nm nm

3. Principle of Superposition: add instantaneous amplitudes
Constructive interference
Destructive interference

4. Diffraction of light wavesDr q

5. Ideal thermal radiator: Blackbody Radiator
observed contiunuous spectrum vs. classical theory:
Ultraviolet Catastrophe IC I l I l

6. Theoretical black body: standing wave modes in a (3-d) cavity

7. Example 2.1 A certain 660 Hz tuning fork can be considered as a harmonic oscillator with a vibrational energy of 0.04J. Compare its energy quantum of energy for the tuning fork with its vibrational energy. Compare the fork’s quantum of energy with those of an atomic oscillator which emits a frequency of 5.00x14 Hz.

8. A
Photoelectric effect
Classical problems:
no delay in emission of electrons
KE of electrons indepentdent of intensity
KE of electrons depends upon frequency of light
effect occurs only above threshold frequency n0
Einstein: quantize light (photons)
1 photon absorbed => 1 photoelectron released
Conservation of Energy

9. Thermionic Emission: kT ~ f => random motion kicks electrons loose
Example 2.2 Ultraviolet light of wavelength 350 nm and an intensity of 1.00 W/m2 is directed at a potassium surface (f = 2.2eV). (a) Find the maximum KE of the photoelectrons. (b) If 0.50 percent of the incident photons produce photoelectrons, how many are emitted per second if the potassium surface area is 1.0 cm2?
Thermionic Emission: kT ~ f
=> random motion kicks electrons loose
Wave-particle “duality”
interference and diffraction: wave phenomena
photoelectric effect, etc.: particle phenomena
=> intensity ~ probability for individual photons

10. X-Ray production: bremsstrahlung (braking radiation)
“inverse” photoelectric effect
1 electron (KE) in => photon (E = hf) out V
maximum energy photon get all of electron’s KE
electron KE from accelerating potential

11. Example 2.3 Find the shortest wavelength present in the radiation from an X-ray machine whose accelerating potential is 50 kV.

12. Typical continuous x-ray spectrum
wavelength l
relative intensity
Typical continuous x-ray spectrum
wavelength l
relative intensity
Some target materials produce sharp maximum in the x-ray spectrum

13. X-ray diffraction: how to measure the wavelength of x-raysqi qr
Constructive Interference when qi = qr (0th order) qi d
Path difference = 2d sin qi
Constructive Interference n l = 2d sin qi
n = 1, 2, 3 ...
note: path deflected by 2q

14. particle nature of light (photons)
Compton effect: an elastic collision between a phton and a charged particle initially at rest e f l’ l q
particle nature of light (photons)
+ (Relativistic) conservation of energy and momentum

15. lC = pm for electrons

16. Example 2. 4 X-rays of wavelength 10. 0 pm are scattered from a target
Example 2.4 X-rays of wavelength 10.0 pm are scattered from a target. (a) Find the wavelength of the x-rays scattered through an angle of 45 degrees. (b) Find the maximum wavelength of the scattered x-rays. (c) Find the maximum KE of the recoil electrons.

17. conservation of energy, momentum + other conservation laws E = mc2
pair production:
conservation of energy, momentum + other conservation laws
E = mc2 N l e p
e +
e -
creation of particle and antiparticle (antimatter)
antiparticle has same mass, opposite charge etc.
particle/antiparticle pair can anihilate to create a pair of photons: e + + e - -> g + g

18. Example 2. 5: Show that pair production cannot occur in empty space
Example 2.5: Show that pair production cannot occur in empty space. (Hint: look at relativistic conservation of energy and momentum)
Example 2.6: An electron and a positron are moving side by side in the +x direction at 0.500c when they annihilate each other. Two photons are produced that move along the x -axis. (a) Do both photons move in the +x direction? (b) What is the energy of each photon?

19. Photon Absorption
Three chief mechanisms for x-ray and gamma ray photons to interact with matter
photoelectric effect (photon absorbed)
Compton scattering (photon energy decreased)
pair production (photon converted to pair)
The dominant mechanism depends upon material and photon energy
A slab of material will reduce intensity:

20. Example 2. 7: The linear attenuation coefficient for 2
Example 2.7: The linear attenuation coefficient for 2.0 MeV gamma rays in water is 4.9 m-1. (a) Find the relative intensity of the gamma rays after it has passed through 10 cm of water. (b) How far must the beam travel in water before being reduced to 1 percent of its original value?
Problems: 2,5,6,8,11,12,15,17,19,20,21,22,23,26,27,29,32,39,43,45,46,47
skip 2.9 or read at your liesure