17 PROBING DEEP INTO MATTER Creation and Annihilation

1. 17 PROBING DEEP INTO MATTERCreation and Annihilation • Describe differences between matter and antimatter • Apply conservation laws to annihilation and materialisation events • Explain how antimatter is used in medical imaging (PET) Starter: Can you give reasons why imaging the brain using x rays may have limitations or drawbacks.

2. Conventional x ray imaging does not show soft tissue well • Conventional x ray imaging is a “2 dimensional” technique • Computerised axial tomography can give 3D information but x ray dose is higher than conventional x ray imaging • X ray techniques cannot map brain activity, only show structures

3. Read pages 189-191 Answer the following: • What does PET stand for? • Try and summarise in you own words how it works. 3) What is the main difference between matter and antimatter? What is the one thing that is the same? Ext: 4) What is meant by creation, annihilation and pair production?

4. Energy, momentum and Electric Charge conserved

6. Annihilation and Creation

7. Pair Production

8. Starter… An electron and a positron with negligible kinetic energy annihilate and produce two identical gamma ray photons. (Rest mass of electron =9.11x10-31kg, h=6.63x10-34Js, c = 3x108 ms-1) Calculate a) the energy released (in J and MeV) b) the frequency of the gamma-photons (in Hz).

9. Particle interactions • Describe how charged particles interact via virtual photon exchange • Explain how to describe these processes using Feynman diagrams and the “try all paths” approach • Discuss consequences of the differences between fermions and bosons Starter: What are the maximum and minimum amplitudes that can result from adding two phasors, each of length 1 unit, and what are the phase differences in each case?

10. Starter: Explain the point this diagram is making…. “Try all paths” is a quantum rule obeyed by all photons and electrons. The same idea is applied to interactions of particles. Richard Feynman invented a type of diagram to help physicists keep track of all the possible ways that particles can interact. The rule “try all paths” changes to “try everything allowed” or more technically “everything that is not forbidden is compulsory”. Source Detector

14. To find out.......... What is a fermion? Give an example of a particle that is a fermion. What happens if you try to squeeze two fermions into the same region of space? Can you describe one important consequence of this? What is a boson? Give an example of a particle that is a boson. What happens if two identical bosons encounter each other? Can you give one important practical application of this?

15. Electron spin Photon spin

16. Fermions and Bosons Fermions ½ integer spin (1/2, 3/2,....) Electrons, Protons etc. Never occupy same quantum state (Avoid each other always) Consequently..... • Two electrons in same orbital of an atom must have opposite spin (Pauli exclusion principle) • Matter is “hard”: atoms are difficult to squash! Bosons Integer spin (0,1,...) Photons Can occupy same quantum state (Can “flock” together in step) Consequently..... • In a laser, lots of photons join together to produce beam of photons all of identical phase and polarisation

18. Fermions and Bosons Fermions ½ integer spin (1/2, 3/2,....) Electrons, Protons etc. Never occupy same quantum state (Avoid each other always) Consequently..... • Two electrons in same orbital of an atom must have opposite spin (Pauli exclusion principle) • Matter is “hard”: atoms are difficult to squash! Bosons Integer spin (0,1,...) Photons Can occupy same quantum state (Can “flock” together in step) Consequently..... • In a laser, lots of photons join together to produce beam of photons all of identical phase and polarisation

19. Light Amplification by Stimulated Emission of Radiation

20. Starter For each of the following statements, say whether it applies to FERMIONS or BOSONS: Q1. A photon is an example of this class of particle. Q2. These particles have integer spin values. Q3. Particles which cannot occupy the same quantum state. Q4. “Matter” particles, like protons, neutrons and electrons belong to this class. Q5. Virtual particles which are exchanged between interacting matter particles belong to this class. Q6. These particles can have spin values of 1/2, 3/2, 5/2 etc. Q7. (For chemistry students): Two electrons cannot occupy the same quantum state. How is it then possible to get two electrons into the same orbital? Hint: in what way are the two electrons distinguishable when in the same orbital?

21. Conservation in nuclear processes • Explain why a new particle was needed to account for the energy spectrum of beta particles • Balance nuclear equations: charge, mass-energy, baryon number, lepton number

22. The Baryon Family Baryons contain three quarks (we come to them later). Protons and neutrons are baryons! Baryon number must be conserved. Baryon number is +1 for all protons and -1 for anti-protons. Note: Protons and neutrons are also described as nucleons.

23. Leptons – fundamental particles Leptons are fundamental particles. As far as we are aware they are not made up of anything smaller. Examples are electrons and neutrinos. Leptons are given a property called lepton number. Electrons and neutrinos are given lepton number 1. Where as the antiparticles are given lepton number -1. All hadrons (non-leptons, which we learn more about later) have lepton number 0.

25. Rutherford’s experiment • Describe how alpha scattering changed our view of atomic structure • Explore effects of changing alpha particle energy and nuclear charge on scattering • Estimate upper limit on nuclear size

26. Starter: Q1. I have a charge of +1 and a lepton number of -1. What could I be? Q2. I have a charge of zero and a lepton number of +1. What could I be? Q3. I have a baryon number of +1, a lepton number of zero and a charge of +1. What could I be? Q4. I have a baryon number of +1 and a charge of zero. What could I be? Q5. I have a baryon number of -1 and a charge of -1. What could I be?

27. Starter: Q1. I have a charge of +1 and a lepton number of -1. What could I be? ANTIELECTRON (POSITRON) Q2. I have a charge of zero and a lepton number of +1. What could I be? NEUTRINO Q3. I have a baryon number of +1, a lepton number of zero and a charge of +1. What could I be? PROTON Q4. I have a baryon number of +1 and a charge of zero. What could I be? NEUTRON Q5. I have a baryon number of -1 and a charge of -1. What could I be? ANTIPROTON

28. Gravitational and electric fields compared Q1. (a) Write down the expression for the force F between two masses, M and m, separated by a distance R. Q1. (b) Write down the corresponding expression for the force F between two charges Q and q, separated by a distance R. (The constant in the equation is known as the electric force constant, and is denoted by k.) Q2. (a) Write down the expression for the gravitational potential energy for an object of mass m at a distance R from the centre of a planet of mass M. Q2. (b) Write down the corresponding expression for the gravitational potential energy of a charge +q at a distance R from another charge +Q. Q3. (a) How much kinetic energy would you need to give the object in Q2. (a) for it to be able to “climb out” of the potential well of the planet? Q3. (b) How much kinetic energy would the charge +q in Q3. (a) have if it was released and allowed to coast far away from +Q?

29. Rutherford’s experiment Note: an alpha particle Is a helium nucleus with the electrons removed. So it is positively charged!

30. Copy and complete the table using the statements provided the nucleus is positively charged, while the electrons are outside it, far away nearly all the mass of the atom is in thenucleus there must be centres of + charge in the atom the nucleus is tiny compared to the overall size of the atom the atom is mostly empty space the centres of + charge must be much heavier than the alpha particles

36. Measuring the size of nuclei • Explain how electron diffraction can be used to measure nuclear size accurately and precisely • Determine nuclear diameter from scattering curves • Describe and explain the relationship between nuclear size and nucleon number Starter: From your AS physics waves knowledge, explain the appearance of all features of the single-slit diffraction curve shown below:

37. JJ and GP Thomson: father and son Nobel physics prize winners Whatever, Dad. I got it for showing that the electron is a wave! Listen sonny, I got the Nobel prize for showing that the electron is a particle...

38. Wave-particle duality

39. Electron diffraction This eerie green glow is caused by low energy electrons in a cathode ray tube striking the phosphorescent coating on the inside of the glass bulb just behind the ruler.  • In this case the diffraction is caused by the electrons passing through a thin layer of polycrystalline graphite (pencil "lead"). The regular array of carbon atoms in the crystals is responsible for the diffraction effects.

40. How does the electron energy affect what is seen in an electron diffraction experiment? Diffraction of low energy electrons Diffraction by planes of atoms of low energy electrons gives a diffraction pattern that reveals the inter atomic spacing. Here, the de Broglie wavelength of the electrons is quite large, as their momentum is small. The wavelength is comparable to the inter atomic spacing, so we get a lot of diffraction by the planes of atoms in the manner of a diffraction grating diffracting light. Diffraction of high energy electrons With very high energy electrons, the de Broglie wavelength is comparable to the size of a nucleus, and the diffraction effects seen are essentially the same as single slit diffraction. The atomic nucleus behaves as an obstacle for the electrons to diffract around, and the diffraction patterns seen is essentially the same as we get when light passes through a single slit.

41. Electron diffraction Q1. Explain why there is a minimum in the curve. Q2. What would be the effect on the curve of using higher energy electrons? Q3. What would be the effect on the curve of using a sample of argon-40 in place of neon-20?

43. KEY POINT Volume of nucleus is proportional to number of particles it contains.

44. Nuclear density questions... Q1. If nuclear volume is proportional to the number of nucleons (A) in the nucleus, explain why nuclear radius r is given by: r = r0 A1/3where r0 is a constant. Q2. The nucleon number of a gold nucleus is 197. • The radius of the nucleon is 1.2x10-15m. Calculate the radius r of the gold nucleus. • Calculate volume of the gold nucleus. • The mass of a nucleon is 1.67x10-27kg, calculate the nuclear density. Q3. Silver has a mass number of 108. What is its nuclear density?

45. The structure of nucleons • Explain why electrons are well suited to be a probe of nucleon structure • Deduce the quark composition of a range of hadrons (baryons and mesons) Starter: Explain why alpha particles and protons are not well suited to probing the size of nuclei

48. Particle Family Tree As we currently understand!!

49. Quarks The building blocks of protons and neutrons, and other fundamental particles. Two flavours of quark… The up quark (+ 2/3 e) and the down quark (– 1/3 e). The first direct evidence for quarks was obtained when very high-energy electrons (approx. 20Gev) in a beam were scattered from a stationary target as if there were point-like scattering centres in each proton or neutron. Quarks do not exist in isolation. They are bound together by the exchange of gluons(since they are the glue that hold the quarks together).