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E y. B z. x. Chapter 2: Particle Properties of Waves. Electromagnetic Waves coupled Electric and Magnetic Oscillations harmonic waves a.k.a. sine waves. 10 0. 10 5. 10 10. 10 15. 10 20. 10 25. microwave. millimeter. infrared. visible. ultraviolet. x-ray. Gamma. Radio. 10 5.

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

  2. 100 105 1010 1015 1020 1025 microwave millimeter infrared visible ultraviolet x-ray Gamma Radio 105 100 10-5 10-10 10-15 • electromagnetic spectrum • l = c/f f (Hz) l (m) 4.3 x1014 - 7.5 x1014 (Hz) Visible Light ROYGBIV 700 nm - 400 nm

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

  4. r1 S1 d r2 S2 Dr q Diffraction of light waves

  5. I l Ideal thermal radiator: Blackbody Radiator IC observed contiunuous spectrum vs. classical theory: Ultraviolet Catastrophe 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. 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. V • X-Ray production: bremsstrahlung (braking radiation) • “inverse” photoelectric effect • 1 electron (KE) in => photon (E = hf) out • 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. relative intensity wavelength l relative intensity wavelength l Typical continuous x-ray spectrum Some target materials produce sharp maximum in the x-ray spectrum

  13. X-ray diffraction: how to measure the wavelength of x-rays qi 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. l’ f e q e l e Compton effect: an elastic collision between a phton and a charged particle initially at rest particle nature of light (photons) + (Relativistic) conservation of energy and momentum

  15. lC = 2.426 pm for electrons

  16. 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. p l N e • pair production: • conservation of energy, momentum + other conservation laws • E = mc2 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. (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 2.0 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

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