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  1. Notice of first test • Please be notified that we will hold our first test on 16 Jan 2004, Friday, 5.00 – 5.50 pm (which was previously scheduled for the 3rd tutorial). • The test paper comprises of 20 objective questions on (1) SR, (2) particle properties of radiation, (3) wave properties of particles. Tutors will monitor the process of the test. • Please make sure that you bring along your pencil can scientific calculator, and don’t miss the test. Thanks.

  2. Notification of “ Constructive Web-Based Learning” • Please be notified that the “computer-based test” as mentioned earlier on is now ready • Each student taking the course ZCT 104/3E please fill up your name in the registration lists that have been put up outside the “Makmal Kumputer Fizik Gunaa” in the 2nd level, School of Physics • You only need to sit the “test” once. The “test” will be lasting for about an hour. No prior preparation is needed • The dates this test will be conducted are as the followed (choose a date and time that suits your preference) • 3/1/04 (Sat) 4/1/04 (Sun) 9/1/04 (Fri) • 10/1/04 (Sat) 11/1/04 (Sun) 17/1/04 (Sat) • 18/1/04 (Sun)

  3. Pair Production: Energy into matter

  4. Conservational laws in pair-production • The pair-production must not violate some very fundamental laws in physics: • Charge conservation, total linear momentum, total relativistic energy are to be obeyed in the process • Due to kinematical consideration (energy and linear momentum conservations) pair production cannot occur in empty space • Must occur in the proximity of a nucleus (check out the detail yourself in the text book if interested)

  5. Energy threshold • Due to conservation of relativistic energy, pair production can only occur if Eg is larger than 2 me = 2 x 0.51 MeV = 1.02 MeV • Any additional photon energy becomes kinetic energy of the electron and positron, K PP nucleus

  6. Example • What is the minimal wavelength of a EM radiation to pair-produce an electron-positron pair? • Solutions: minimal photon energy occurs if the pair have no kinetic energy after being created, K = 0 • Hence, These are very energetic EM radiation called gamma rays and are found in nature as one of the emissions from radioactive nuclei and in cosmic rays.

  7. Pair-annihilation • The inverse of pair production occurs when a positron is near an electron and the two come together under the influence of their opposite electric charges e+ + e-g + g • Both particles vanish simultaneously, with the lost masses becoming energies in the form of two gamma-ray photons:

  8. Final energy = hc/l + hc/l Initial energy = 2mec2 + K Conservation of relativistic energy: 2mec2 + K = 2 hc/l

  9. The total relativistic energy of the e--e+ pair is E = 2mec2 + K = 1.02 MeV + K, where K the total kinetic energy of the electron-positron pair before annihilation • Each resultant gamma ray photon has an energy hn = 0.51 MeV + K/2 • Both energy and linear momentum are automatically conserved in pair annihilation (else it wont occur at all) • The gamma photons are always emitted in a back-to-back manner due to kinematical reasons (conservation of linear momentum) • No nucleus or other particle is needed for pair annihilation to take place • Pair annihilation always occurs whenever a matter comes into contact with its antimatter

  10. As a tool to observe anti-world • What is the characteristic energy of a gamma-ray that is produced in a pair-annihilation production process? What is its wavelength? • Answer: 0.51 MeV, lannih = hc / 0.51 MeV = 0.0243 nm • The detection of such characteristic gamma ray in astrophysics indicates the annihilation of matter-antimatter in deep space • May indicate the existence of ‘anti-matter world’ • However, none of this is observed • Our observed universe does not contain any anti-matter world

  11. Wave particle duality • “Quantum nature of light” refers to the particle attribute of light • “Quantum nature of particle” refers to the wave attribute of a particle • Light (classically EM waves) is said to display “wave-particle duality” – it behave like wave in one experiment but as particle in others (c.f. a person with schizophrenia)

  12. Not only light does have “schizophrenia”, so are other microscopic ``particle’’ such as electron, (see later chapters), i.e. particle” also manifest wave characteristics in some experiments • Wave-particle duality is essentially the manifestation of the quantum nature of things • This is an very weird picture quite contradicts to our conventional assumption with is deeply rooted on classical physics or intuitive notion on things

  13. When is light wave and when is it particle? • Whether light displays wave or particle nature depends on the object it is interacting with, and also on the experimental set-up to observe it • If an experiment is set-up to observe the wave nature (such as in interference or diffraction experiment), it displays wave nature • If the experimental set-up has a scale that is corresponding to the quantum nature of radiation, then light will displays particle behaviour, such as in Compton scatterings

  14. Compton wavelength as a scale to the quantum nature of light and matter (electron) • As an example of a ‘scale’ in a given experiment or a theory, let’s consider the Compton wavelength in Compton scattering • Compton wavelength is the lengthscale which characterises the onset of quantum nature of light (corpuscular nature) and electron (wave nature) in their interactions

  15. If the wavelength of light is much larger than the Compton wavelength of the electron it is interacting with, light behaves like wave (e.g. in interference experiments with visible light). Compton effect is negligible in this case • On the other hand, if the wavelength of the radiation is comparable to the Compton wavelength of the interacting particle, light starts to behave like particle and collides with the electron in an ‘particle-particle’ manner

  16. In short the identity manifested by light depends on what it “sees” (which in turns depend on its own wavelength) in a given experimental condition Microscopic matter particle (such as electron and atoms) also manifest wave-particle duality This will be the next agenda in our course

  17. Wavelike properties of particle • In 1923, while still a graduate student at the University of Paris, Louis de Broglie published a brief note in the journal Comptes rendus containing an idea that was to revolutionize our understanding of the physical world at the most fundamental level: That particle has intrinsic wave properties • For more interesting details: • Prince de Broglie, 1892-1987

  18. de Broglie’s postulate (1924) • The postulate: there should be a symmetry between matter and wave. The wave aspect of matter is related to its particle aspect in exactly the same quantitative manner that is in the case for radiation. The total energy E and momentum p of an entity, for both matter and wave alike, is related to the frequency n of the wave associated with its motion via by Planck constant • E = hn; p = h/l

  19. A particle with momentum p is pictured as a wave Matter wave with de Broglie wavelength l = p/h Particle with linear momentum p l= h/p • is the de Broglie relation predicting the wave length of the matter wave l associated with the motion of a material particle with momentum p

  20. A physical entity possess both aspects of particle and wave in a complimentary manner BUT why is the wave nature of material particle not observed? Because …

  21. Because…we are too large and quantum effects are too small • Consider two extreme cases: • (i) an electron with kinetic energy K = 54 eV, de Broglie wavelenght, l = h/p = h / (2meK)1/2 = 1.65 Angstrom • (ii) a billard (100 g) ball moving with momentum p = mv = 0.1 kg x 10 m/s = 1 Ns, de Broglie wavelenght, l = h/p = 10-34 m, too small to be observed in any experiments

  22. Matter wave is a quantum phenomena • This also means that this effect is difficult to observe in our macroscopic world (unless with the aid of some specially designed apparatus) • The smallness of h in the relation l = h/p makes wave characteristic of particles hard to be observed • The statement that when h  0, l becomes vanishingly small means that • the wave nature will becomes effectively ``shut-off’’ and there would appear to loss its wave nature whenever the relevant scale (e.g. the p of the particle) is too large in comparison with h ~ 10-34 Js • In other words, the wave nature will of a particle will only show up when the scale p is comparable (or smaller) to the size of h