1. Chapter 29 Nuclear Physics

2. Topics in nuclear physics include – Properties and structure of atomic nuclei – Radioactivity – Nuclear reactions Decay processes Fission Fusion Introduction

3. Ernest Rutherford 1871 – 1937 Discovery that atoms could be broken apart Studied radioactivity Nobel prize in 1908 Section 29.1

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. Section 29.1

5. Symbolism Symbol: – 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 Z may be omitted since the element can be used to determine Z. Section 29.1

6. More Properties The nuclei of all atoms of a particular element must contain the same number of protons. They may contain varying numbers of neutrons. – Isotopes of an element have the same Z but differing N and A values. – Example, isotopes of carbon:

7. Charge The proton has a single positive charge, +e The electron has a single negative charge, -e – e = 1.602 177 33 x 10 -19 C The neutron has no charge. – Makes it difficult to detect Section 29.1

8. Mass It is convenient to use unified mass units, u, to express masses. – Based on definition that the mass of one atom of C-12 is exactly 12 u – 1 u = 1.660 559 x 10 -27 kg Mass can also be expressed in MeV/c 2 – From E R = m c 2 – 1 u = 931.494 MeV/c 2 Section 29.1

9. Summary of Masses Section 29.1

10. The Size of the Nucleus First investigated by Rutherford in scattering experiments He found an expression for how close an alpha particle moving toward the nucleus can come before being turned around by the Coulomb force. The KE of the particle must be completely converted to PE. Section 29.1

11. Size of the Nucleus, Cont. d gives an upper limit for the size of the nucleus. Rutherford determined that – For gold, he found d = 3.2 x 10 -14 m – For silver, he found d = 2 x 10 -14 m Such small lengths are often expressed in femtometers where 1 fm = 10 -15 m – Also called a fermi Section 29.1

12. Size of Nucleus, Current Since the time of Rutherford, many other experiments have concluded: – Most nuclei are approximately spherical. – Average radius is r o = 1.2 x 10 -15 m A is the number of nucleons. Section 29.1

13. 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 have nearly the same density. Nucleons combine to form a nucleus as though they were tightly packed spheres. Section 29.1

14. Maria Goeppert-Mayer 1906 – 1972 Best known for her development of shell model of the nucleus Shared Nobel Prize in 1963 Section 29.1

15. 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. Section 29.1

16. Nuclear Stability, Cont. Light nuclei are most stable if N = Z. Heavy nuclei are most stable when N > Z. – As the number of protons increases, the Coulomb force increases and so more nucleons are needed to keep the nucleus stable. No nuclei are stable when Z > 83. Section 29.1

17. Binding Energy The total mass of a nucleus is always less than the sum of the masses of its nucleons. 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. Section 29.2

18. Binding Energy per Nucleon Section 29.2

19. 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. Section 29.2

20. Marie Curie 1867 – 1934 Discovered new radioactive elements Shared Nobel Prize in physics in 1903 – For study of radioactive substances Nobel Prize in Chemistry in 1911 – For the discovery of radium and polonium Section 29.3

21. Radioactivity Radioactivity is the spontaneous emission of radiation. Experiments suggested that radioactivity was the result of the decay, or disintegration, of unstable nuclei. Section 29.3

22. Radioactivity – Types Three types of radiation can be emitted – Alpha particles The particles are 4 He 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. Section 29.3

23. Distinguishing Types of Radiation A radioactive beam is directed into a region with a magnetic field. The gamma particles carry no charge and thus are not deflected. The alpha particles are deflected upward. The negative beta particles (electrons) are deflected downward. – Positrons would be deflected upward. Section 29.3

24. 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 Section 29.3

25. 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. Section 29.3

26. Decay Curve The decay curve follows the equation – N = N o 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. Section 29.3

27. Note About Half-Life During one half-life, half of a given number of nuclei will decay. During a second half-life, half of the remaining number of nuclei will decay. – This would be three-quarters of the original number of nuclei. Section 29.3

28. Units The unit of activity, R, is the Curie, Ci – 1 Ci = 3.7 x 10 10 decays/second The SI unit of activity is the Becquerel, Bq – 1 Bq = 1 decay / second Therefore, 1 Ci = 3.7 x 10 10 Bq The most commonly used units of activity are the mCi and the µCi Section 29.3

29. 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. Section 29.4

30. 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. Section 29.4

31. Decay – General Rules When one element changes into another element, the process is called spontaneous decay or transmutation. The sum of the mass numbers, A, must be the same on both sides of the equation. The sum of the atomic numbers, Z, must be the same on both sides of the equation. Conservation of mass-energy and conservation of momentum must hold. Section 29.4

32. Beta Decay During beta decay, the daughter nucleus has the same number of nucleons as the parent, but the atomic number is changed by one. Symbolically Section 29.4

33. Beta Decay, Cont. 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. Section 29.4

34. Beta Decay – Electron Energy The energy released in the decay process should almost all go to kinetic energy of the electron (KE max ) Experiments showed that few electrons had this amount of kinetic energy. Section 29.4

35. Neutrino To account for this “missing” energy, in 1930 Pauli proposed the existence of another particle. – Also needed in order to conserve momentum Enrico Fermi later named this particle the neutrino. Properties of the neutrino – Zero electrical charge – Mass much smaller than the electron, recent experiments indicate definitely some mass – Spin of ½ – Very weak interaction with matter Section 29.4

36. Enrico Fermi 1901 – 1954 Produced transuranic elements Other contributions – Theory of beta decay – Free-electron theory of metals – World’s first fission reactor (1942) Nobel Prize in 1938 Section 29.4

37. 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 Section 29.4

38. Electron Note Another notation for the electron is – The mass of the electron is so much smaller than the lightest nucleon, it can be approximated as 0 in nuclear reactions and decays. Section 29.4

39. 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 photons are called gamma rays, very high energy relative to light 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. Section 29.4

40. 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. Section 29.4

41. Uses of Radioactivity Carbon Dating – Beta decay of 14 C is used to date organic samples. – The ratio of 14 C to 12 C 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. Section 29.4

42. More Uses of Radioactivity Radon detection – 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 Section 29.4

43. 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 See table 29.2 Section 29.5

44. Decay Series of 232 Th Series starts with 232 Th Processes through a series of alpha and beta decays Ends with a stable isotope of lead, 208 Pb Section 29.5

45. 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. Section 29.6

46. Nuclear Reactions – Example Alpha particle colliding with nitrogen: Balancing the equation allows for the identification of X So the reaction is Section 29.6

47. 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. Section 29.6

48. 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 incident particle. – M is the mass of the target particle. If the energy is less than this amount, the reaction cannot occur. Section 29.6

49. 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. Section 29.7

50. 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 Section 29.7

51. Units of Radiation Exposure Roentgen [R] – That amount of ionizing radiation that will produce 2.08 x 10 9 ion pairs in 1 cm 3 of air under standard conditions – That amount of radiation that deposits 8.76 x 10 -3 J of energy into 1 kg of air Rad (Radiation Absorbed Dose) – That amount of radiation that deposits 10 -2 J of energy into 1 kg of absorbing material – Has generally replaced the roentgen Section 29.7

52. 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 – See table 29.3 for some RBE factors Rem (Roentgen Equivalent in Man) – Defined as the product of the dose in rad and the RBE factor Dose in rem = dose in rad X RBE Section 29.7

53. 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. Section 29.7

54. Applications of Radiation Sterilization – Used to destroy bacteria, worms and insects in food – Radiation has been used to sterilize medical equipment. – Bone, cartilage, and skin used in graphs is often irradiated before grafting to reduce the chances of infection. Section 29.7

55. Applications of Radiation, Cont. Tracing – Radioactive particles can be used to trace chemicals participating in various reactions. Example, 131 I to test thyroid action – Can be used to locate a hemorrhage inside the body – Check the absorption of fluorine by teeth – Checking contamination of food-processing equipment – Monitoring deterioration inside an automobile engine Section 29.7

56. Applications of Radiation, Final MRI – Magnetic Resonance Imaging – When a nucleus having a magnetic moment is placed in an external magnetic field, its moment precesses about the magnetic field with a frequency that is proportional to the field. – Transitions between energy states can be detected electronically.

57. MRI, Example