Chapter 29

1. Chapter 29 Nuclear Physics

2. Milestones in the Development of Nuclear Physics • 1896 – Becquerel discovered radioactivity in uranium compounds • Rutherford showed the radiation had three types • Alpha (He nucleus) • Beta (electrons) • Gamma (high-energy photons) • 1911 Rutherford, Geiger and Marsden • Established the point mass nature of the nucleus • Nuclear force was a new type of force • 1919 Rutherford and coworkers first observed nuclear reactions in which naturally occurring alpha particles bombarded nitrogen nuclei to produce oxygen

3. Milestones • 1932 Cockcroft and Walton first used artificially accelerated protons to produce nuclear reactions • 1932 Chadwick discovered the neutron • 1933 the Curies discovered artificial radioactivity • 193 Hahn and Strassman discovered nuclear fission • 1942 Fermi and collaborators achieved the first controlled nuclear fission reactor

4. Some Properties of Nuclei • All nuclei are composed of protons and neutrons • Exception is ordinary hydrogen with just a proton • The atomic number, Z, equals the number of protons in the nucleus • The neutron number, N, is the number of neutrons in the nucleus • The mass number, A, is the number of nucleons in the nucleus • A = Z + N • Nucleon is a generic term used to refer to either a proton or a neutron • The mass number is not the same as the mass

5. Symbolism • X is the chemical symbol of the element • Example: • Mass number is 27 • Atomic number is 13 • Contains 13 protons • Contains 14 (27 – 13) neutrons • The atomic number, Z, may be omitted since the element can be used to determine Z

6. Isotopes • Isotopes of an element have the same Z but differing N and A values • Example:

7. Charge • The proton has a single positive charge, +e • The electron has a single negative charge, -e • The neutron has no charge • Makes it difficult to detect • e = 1.60217733 x 10-19 C

8. Mass • It is convenient to use atomic mass units, u, to express masses • 1 u = 1.660559 x 10-27 kg • Based on definition that the mass of one atom of C-12 is exactly 12 u • Mass can also be expressed in MeV/c2 • From ER = m c2 • 1 u = 931.494 MeV/c2

9. Summary of Masses

10. The Size of the Nucleus • First investigated by Rutherford in scattering experiments • The KE of the particle must be completely converted to PE • d gives an upper limit for the size of the nucleus • For gold, d = 3.2 x 10-14 m • For silver, d = 2 x 10-14 m • d is often expressed in femtometers; 1 fm = 10-15 m (also called a fermi)

11. Size of Nucleus, Current • Since the time of Rutherford, many other experiments have concluded the following • Most nuclei are approximately spherical • Average radius is • ro = 1.2 x 10-15 m

12. Density of Nuclei • The volume of the nucleus (assumed to be spherical) is directly proportional to the total number of nucleons • This suggests that all nuclei havenearly the same density • Nucleons combine to form a nucleus as though they were tightly packed spheres

13. Nuclear Stability • There are very large repulsive electrostatic forces between protons • These forces should cause the nucleus to fly apart • The nuclei are stable because of the presence of another, short-range force, called the nuclear force • This is an attractive force that acts between all nuclear particles • The nuclear attractive force is stronger than the Coulomb repulsive force at the short ranges within the nucleus

14. Nuclear Stability, cont • Light nuclei are most stable if N = Z • Heavy nuclei are most stable when N > Z • As the number of protons increase, the Coulomb force increases and so more nucleons are needed to keep the nucleus stable • No nuclei are stable when Z > 83

15. Binding Energy • The total energy of the bound system (the nucleus) is less than the combined energy of the separated nucleons • This difference in energy is called the binding energy of the nucleus • It can be thought of as the amount of energy you need to add to the nucleus to break it apart into separated protons and neutrons

16. Binding Energy per Nucleon

17. Binding Energy Notes • Except for light nuclei, the binding energy is about 8 MeV per nucleon • The curve peaks in the vicinity of A = 60 • Nuclei with mass numbers greater than or less than 60 are not as strongly bound as those near the middle of the periodic table • The curve is slowly varying at A > 40 • This suggests that the nuclear force saturates • A particular nucleon can interact with only a limited number of other nucleons

18. Radioactivity • Radioactivity is the spontaneous emission of radiation • Experiments suggested that radioactivity was the result of the decay, or disintegration, of unstable nuclei

19. Radioactivity – Types • Three types of radiation can be emitted • Alpha particles • The particles are 4He nuclei • Beta particles • The particles are either electrons or positrons • A positron is the antiparticle of the electron • It is similar to the electron except its charge is +e • Gamma rays • The “rays” are high energy photons

20. Distinguishing Types of Radiation • The gamma particles carry no charge • The alpha particles are deflected upward • The beta particles are deflected downward

21. Penetrating Ability of Particles • Alpha particles • Barely penetrate a piece of paper • Beta particles • Can penetrate a few mm of aluminum • Gamma rays • Can penetrate several cm of lead

22. The Decay Constant • The number of particles that decay in a given time is proportional to the total number of particles in a radioactive sample • ΔN = -λ N Δt • λ is called the decay constant and determines the rate at which the material will decay • The decay rate or activity, R, of a sample is defined as the number of decays per second

23. Decay Curve • The decay curve follows the equation • N = No e- λt • The half-life is also a useful parameter • The half-life is defined as the time it takes for half of any given number of radioactive nuclei to decay

24. Units • The unit of activity, R, is the Curie, Ci • 1 Ci = 3.7 x 1010 decays/second • The SI unit of activity is the Becquerel, Bq • 1 Bq = 1 decay / second • 1 Ci = 3.7 x 1010 Bq • The most commonly used units of activity are the mCi and the µCi

25. What fraction of a radioactive sample has decayed after two half-lives have elapsed? (a) 1/4 (b) 1/2 (c) 3/4 (d) not enough information to say QUICK QUIZ 29.1

26. The activity of a newly discovered radioactive isotope reduces to 96% of its original value in an interval of 2 hours. What is its half-life? (a) 10.2 h (b) 34.0 h (c) 44.0 h (d) 68.6 h QUICK QUIZ 29.2

27. Alpha Decay • When a nucleus emits an alpha particle it loses two protons and two neutrons • N decreases by 2 • Z decreases by 2 • A decreases by 4 • Symbolically • X is called the parent nucleus • Y is called the daughter nucleus • When one element changes into another element, the process is called spontaneous decay or transmutation

28. Alpha Decay -- Example • Decay of 226 Ra • Half life for this decay is 1600 years • Excess mass is converted into kinetic energy • Momentum of the two particles is equal and opposite

29. If a nucleus such as226Ra that is initially at rest undergoes alpha decay, which of the following statements is true? (a) The alpha particle has more kinetic energy than the daughter nucleus. (b) The daughter nucleus has more kinetic energy than the alpha particle. (c) The daughter nucleus and the alpha particle have the same kinetic energy. QUICK QUIZ 29.3

30. Beta Decay • During beta decay, the daughter nucleus has the same number of nucleons as the parent, but the atomic number is one less • Symbolically • The emission of the electron is from the nucleus • The nucleus contains protons and neutrons • The process occurs when a neutron is transformed into a proton and an electron • Energy must be conserved

31. Beta Decay – Electron Energy • The energy released in the decay process should almost all go to kinetic energy of the electron • Experiments showed that few electrons had this amount of kinetic energy

32. Neutrino • To account for this “missing” energy, in 1930 Pauli proposed the existence of another particle • Enrico Fermi later named this particle the neutrino • Properties of the neutrino • Zero electrical charge • Mass much smaller than the electron, probably not zero • Spin of ½ • Very weak interaction with matter

33. Beta Decay – Completed • Symbolically •  is the symbol for the neutrino • is the symbol for the antineutrino • To summarize, in beta decay, the following pairs of particles are emitted • An electron and an antineutrino • A positron and a neutrino

34. Gamma Decay • Gamma rays are given off when an excited nucleus “falls” to a lower energy state • Similar to the process of electron “jumps” to lower energy states and giving off photons • The excited nuclear states result from “jumps” made by a proton or neutron • The excited nuclear states may be the result of violent collision or more likely of an alpha or beta emission

35. Gamma Decay – Example • Example of a decay sequence • The first decay is a beta emission • The second step is a gamma emission • The C* indicates the Carbon nucleus is in an excited state • Gamma emission doesn’t change either A or Z

36. Uses of Radioactivity • Carbon Dating • Beta decay of 14C is used to date organic samples • The ratio of 14C to 12C is used • Smoke detectors • Ionization type smoke detectors use a radioactive source to ionize the air in a chamber • A voltage and current are maintained • When smoke enters the chamber, the current is decreased and the alarm sounds

37. More Uses of Radioactivity • Radon pollution • Radon is an inert, gaseous element associated with the decay of radium • It is present in uranium mines and in certain types of rocks, bricks, etc that may be used in home building • May also come from the ground itself

38. Natural Radioactivity • Classification of nuclei • Unstable nuclei found in nature • Give rise to natural radioactivity • Nuclei produced in the laboratory through nuclear reactions • Exhibit artificial radioactivity • Three series of natural radioactivity exist • Uranium • Actinium • Thorium

39. Decay Series of 232Th • Series starts with 232Th • Processes through a series of alpha and beta decays • Ends with a stable isotope of lead, 208Pb

40. Nuclear Reactions • Structure of nuclei can be changed by bombarding them with energetic particles • The changes are called nuclear reactions • As with nuclear decays, the atomic numbers and mass numbers must balance on both sides of the equation

41. Which of the following are possible reactions? QUICK QUIZ 29.4

42. Q Values • Energy must also be conserved in nuclear reactions • The energy required to balance a nuclear reaction is called the Q value of the reaction • An exothermic reaction • There is a mass “loss” in the reaction • There is a release of energy • Q is positive • An endothermic reaction • There is a “gain” of mass in the reaction • Energy is needed, in the form of kinetic energy of the incoming particles • Q is negative

43. Threshold Energy • To conserve both momentum and energy, incoming particles must have a minimum amount of kinetic energy, called the threshold energy • m is the mass of the incoming particle • M is the mass of the target particle • If the energy is less than this amount, the reaction cannot occur

44. If the Q value of an endothermic reaction is -2.17 MeV, the minimum kinetic energy needed in the reactant nuclei if the reaction is to occur must be (a) equal to 2.17 MeV, (b) greater than 2.17 MeV, (c) less than 2.17 MeV, or (d) precisely half of 2.17 MeV. QUICK QUIZ 29.5

45. Radiation Damage in Matter • Radiation absorbed by matter can cause damage • The degree and type of damage depend on many factors • Type and energy of the radiation • Properties of the absorbing matter • Radiation damage in biological organisms is primarily due to ionization effects in cells • Ionization disrupts the normal functioning of the cell

46. Types of Damage • Somatic damage is radiation damage to any cells except reproductive ones • Can lead to cancer at high radiation levels • Can seriously alter the characteristics of specific organisms • Genetic damage affects only reproductive cells • Can lead to defective offspring

47. Units of Radiation Exposure • Roentgen [R] is defined as • That amount of ionizing radiation that will produce 2.08 x 109 ion pairs in 1 cm3 of air under standard conditions • That amount of radiation that deposits 8.76 x 10-3 J of energy into 1 km3 of air • Rad (Radiation Absorbed Dose) • That amount of radiation that deposits 10-2 J of energy into 1 kg of air

48. More Units • RBE (Relative Biological Effectiveness) • The number of rad of x-radiation or gamma radiation that produces the same biological damage as 1 rad of the radiation being used • Accounts for type of particle which the rad itself does not • Rem (Roentgen Equivalent in Man) • Defined as the product of the dose in rad and the RBE factor • Dose in rem = dos in rad X RBE

49. Radiation Levels • Natural sources – rocks and soil, cosmic rays • Background radiation • About 0.13 rem/yr • Upper limit suggested by US government • 0.50 rem/yr • Excludes background and medical exposures • Occupational • 5 rem/yr for whole-body radiation • Certain body parts can withstand higher levels • Ingestion or inhalation is most dangerous

50. Applications of Radiation • Sterilization • Radiation has been used to sterilize medical equipment • Used to destroy bacteria, worms and insects in food • Bone, cartilage, and skin used in graphs is often irradiated before grafting