The structure of the nucleus 07


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The structure of the nucleus 07

  2. 2. NUCLEAR TERMS <ul><ul><li>A specific nucleus can be exactly identified using the following notation: z X A or Z X A . </li></ul></ul><ul><ul><li>X is the symbol of the element. </li></ul></ul><ul><ul><li>Z the atomic number (number of protons). </li></ul></ul><ul><ul><li>A the mass number (number of protons and neutrons). The term ‘nucleon’ refers to the protons or neutrons in the nucleus. </li></ul></ul>
  3. 3. ISOTOPES <ul><li>As early as 1911, it became clear that elements could include atoms of different masses. </li></ul><ul><li>They were named isotopes (from the Greek, isos meaning ‘same’ and topos meaning ‘place’) since, although different, they appear at the same place on the periodic table. </li></ul>
  4. 4. ISOTOPES <ul><li>Remember, if you change the number of protons, you change the element. </li></ul><ul><li>If you change the number of neutrons, you have the same element but a different isotope. </li></ul>
  5. 5. ISOTOPES <ul><li>Isotopes can be shown to exist by the study of the element carbon. They have 6 electrons and 6 protons and so are electrically neutral. </li></ul><ul><li>This accounts for its chemical properties. The number of neutrons can change without altering the chemical properties. </li></ul>
  6. 6. ISOTOPES <ul><li>Most carbon nuclei are unstable, only 6 C 12 and 6 C 13 are stable. </li></ul><ul><li>All the rest will decay naturally to more stable arrangements. </li></ul><ul><li>Unstable isotopes are referred to as radioisotopes as they are radioactive. </li></ul><ul><li>We will discuss radioactivity shortly. </li></ul>
  7. 7. ISOTOPES <ul><li>For all the possible arrangements of protons and neutrons that form nuclei, only about 300 are stable. </li></ul><ul><li>All the others are radioactive and will spontaneously breakdown over time. </li></ul><ul><li>Most isotopes are unstable (radioisotopes). </li></ul>
  8. 8. ISOTOPES <ul><li>Take care not to mix up the words ‘isotope’ and ‘ion’. </li></ul><ul><li>An ion has an unequal number of protons and electrons. It is electrically charged. THIS CHANGES THE CHEMISTRY OF THE ATOM. </li></ul><ul><li>An isotope has a unequal number of protons and neutrons. This DOES NOT CHANGE THE CHEMISTRY OF THE ATOM. </li></ul>
  9. 9. THE NUCLEAR FORCE <ul><li>Most atoms have more than one proton in the nucleus. </li></ul><ul><li>This means that there will be a Coulombic repulsive force. </li></ul><ul><li>Why does the nucleus remain stable and not fall apart? </li></ul><ul><li>This is because there is an attractive force between nucleons called the nuclear force. There are a number characteristics that can be deduced. </li></ul>
  10. 10. THE NUCLEAR FORCE <ul><ul><li> The force must be very strong to overcome electrostatic repulsion. It is 1000 times stronger than the electric force and 10 38 times stronger than gravitational attraction. </li></ul></ul><ul><ul><li> The force is independent of charge. This means the force is the same whether it acts between two protons, two neutrons or a proton and a neutron. </li></ul></ul>
  11. 11. THE NUCLEAR FORCE <ul><ul><li> The force acts over a very short range. Within the nucleus, the force acts between a nucleon and its very nearest neighbours. The range of the force is only about 1 x 10 -15 m or about the diameter of a proton. </li></ul></ul><ul><ul><li>The electric force is different in that it acts between all charged pairs and over any distance. </li></ul></ul>
  12. 12. THE NUCLEAR FORCE <ul><li>This explains why there are only a certain number of elements in the universe. </li></ul><ul><li>As the size of the nucleus increases by adding nucleons, the attractive force acts between neighbours but the repulsive force acts between all protons. </li></ul>
  13. 13. THE NUCLEAR FORCE <ul><li>At some stage, the repulsive force becomes so great that the element becomes unstable. </li></ul><ul><li>This occurs at Z = 83 (Z = atomic number). This means that any element with an atomic number greater than 83 is unstable and is radioactive. </li></ul>
  14. 14. MASS DEFECT <ul><li>The simplest bound nuclear system is the nucleus of deuterium ( 1 H 2 ) that is often called heavy hydrogen. Accurate measurements of the mass of the nucleus have found it to be 3.34374 x 10 -27 kg. </li></ul>
  15. 15. MASS DEFECT <ul><li>Using the accurate measurements of the nucleons, there appears to be a discrepancy in the mass. </li></ul><ul><li>m proton = 1.67268 x 10 -27 kg </li></ul><ul><li>m neutron = 1.67499 x 10 -27 kg </li></ul><ul><li>total mass of 1 H 2 = 3.34767 x 10 -27 kg </li></ul><ul><li>actual mass of 1 H 2 = 3.34374 x 10 -27 kg </li></ul><ul><li>mass difference = 0.00393 x 10 -27 kg </li></ul>
  16. 16. MASS DEFECT <ul><li>This loss appears to come from the process that fuses the proton and neutron together. </li></ul><ul><li>It is 4 times as great as the mass of an electron and too great to be explained as experimental error. </li></ul>
  17. 17. MASS DEFECT <ul><li>In every nucleus there is some missing mass. The correct name for this is ‘mass defect’  m and the calculation requires the rest mass of each particle. </li></ul>
  18. 18. MASS DEFECT <ul><li>Einstein’s special theory of relativity requires that mass increases dramatically at speeds close to the speed of light. </li></ul><ul><li>The increase in mass prohibits any object with mass reaching the speed of light so the value of the mass of an object at rest is used to avoid confusion. </li></ul>
  19. 19. MASS DEFECT <ul><li>The mass defect for a nucleus (  m) is defined as the difference between the rest mass of the atomic nucleus and the sum of the rest masses of its individual nucleons in an unbound state. </li></ul>
  20. 20. BINDING ENERGY <ul><li>Where does this mass go? Einstein’s mass-energy relationship E =  mc 2 gives us the answer. </li></ul><ul><li>The lost mass is converted into either kinetic energy or electromagnetic radiation (as gamma rays). </li></ul><ul><li>Einstein audio on his equation </li></ul>
  21. 21. BINDING ENERGY <ul><li>The law of the conservation of energy should be modified to become the law of conservation of mass-energy. </li></ul><ul><li>If a nucleus loses mass, energy is released by the system. </li></ul><ul><li>Binding Energy </li></ul><ul><li>If a nucleus gains mass, energy is required for the nuclear reaction to occur. </li></ul>
  22. 22. BINDING ENERGY <ul><li>A nucleus is considered to be more stable than individual neutrons or protons. </li></ul><ul><li>Energy is always released when something reverts to its most stable state. </li></ul><ul><li>As an example, remember that electrons give off energy when they drop down to their innermost shells (their most stable energy state). </li></ul>
  23. 23. BINDING ENERGY <ul><li>When separate protons or neutrons join together to form a new nucleus, energy will be released. </li></ul><ul><li>The amount of energy released in a deuterium nucleus ( 1 H 2 ) due to the mass defect is: </li></ul>
  24. 24. BINDING ENERGY <ul><li>E =  mc 2 =3.93 x 10 -30 x (3.0 x 10 8 ) 2 </li></ul><ul><ul><ul><ul><ul><li>= 3.54 x 10 -13 J </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>= 2.2 x 10 6 eV </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>= 2.2 MeV </li></ul></ul></ul></ul></ul><ul><li>This is equal to 2.2 X 10 6 eV !!!! </li></ul><ul><li>Compare this to 1-10 eV when an electron falls to a lower energy level. </li></ul>
  25. 25. BINDING ENERGY <ul><li>This can be written as a formula… </li></ul><ul><li>You can see that the combining of a proton and a neutron makes a deuterium nucleus and gives off 2.2 MeV of energy in the form of a gamma ray. </li></ul><ul><li>This is an EXOTHERMIC REACTION. </li></ul>
  26. 26. BINDING ENERGY <ul><li>To reverse the process, the energy from the mass defect must be added to the nucleus. </li></ul><ul><li>This is usually in the form of a gamma ray or kinetic energy from a particle. This energy is called the binding energy . </li></ul><ul><li>This would be an ENDOTHERMIC REACTION. </li></ul>
  27. 27. BINDING ENERGY <ul><li>The binding energy is the energy equivalent to the mass defect when nucleons bind together to form a nucleus. E b =  mc 2 </li></ul>
  28. 28. BINDING ENERGY <ul><li>The typical value for binding energy of nucleons is 1 to 10 MeV and 1 to 10 eV for electrons. </li></ul><ul><li>It is for this reason that mass defect for electrons are not detected - they are too small (approx. 10 -35 kg). </li></ul>
  29. 29. EXAMPLE 1 <ul><ul><li>(a) Given that the rest mass of a proton is 1.67268 x 10 -27 kg and the rest mass of a neutron is 1.67499 x 10 -27 kg, determine the mass defect for the helium isotope ( 2 He 4 ) whose rest mass is 6.64489 x 10 -27 kg. </li></ul></ul><ul><ul><li>(b) What is the binding energy for the helium nucleus in MeV? </li></ul></ul>
  30. 30. EXAMPLE 1 <ul><ul><li>(c) Compare the answer in (b) to the binding energies of electrons bound to the atom. </li></ul></ul><ul><ul><li>(d) What is the maximum wavelength gamma ray that can be used to disintegrate a helium nucleus into its component protons and neutrons? </li></ul></ul>
  31. 31. EXAMPLE 1 <ul><ul><li>m proton = 1.67268 x 10 -27 kg </li></ul></ul><ul><ul><li>m neutron = 1.67499 x 10 -27 kg </li></ul></ul><ul><ul><li>m helium = 6.64489 x 10 -27 kg </li></ul></ul>
  32. 32. EXAMPLE 1 SOLUTION <ul><ul><li>(a)  m = Z x m p + N x m a - m He </li></ul></ul><ul><ul><li>= (2 x 1.67268 + 2 x 1.67499 -6.64489) x 10 -27 </li></ul></ul><ul><ul><li>= (6.69534 - 6.64489) x 10 -27 </li></ul></ul><ul><ul><li>= 5.045 x 10 -29 kg </li></ul></ul>
  33. 33. EXAMPLE 1 SOLUTION <ul><ul><li>(b) E b =  mc 2 </li></ul></ul><ul><ul><li>=5.05 x 10 -29 x (3.0 x 10 8 ) 2 </li></ul></ul><ul><ul><li>=4.54 x 10 -12 J </li></ul></ul><ul><ul><li>= 2.83 x 10 7 eV </li></ul></ul><ul><ul><li>= 28.3 MeV </li></ul></ul>
  34. 34. EXAMPLE 1 SOLUTION <ul><ul><li>(c) Typical binding energies for the electron in the hydrogen atom were between 1 and 10 eV. This nuclear binding energy is of the order of 10 MeV. This is a factor of a million times as great. </li></ul></ul>
  35. 35. EXAMPLE 1 SOLUTION <ul><ul><li>(d) In order to disintegrate the nucleus, the binding energy must be supplied by the gamma ray. </li></ul></ul><ul><ul><li>E photon = hf = </li></ul></ul><ul><ul><li>The maximum wavelength will correspond to the minimum energy photon, ie. the photon with the energy equal to the binding energy of the nucleus. </li></ul></ul>
  36. 36. EXAMPLE 1 SOLUTION = 4.38 x 10 -14 m
  37. 37. EXAMPLE 1 SOLUTION <ul><li>Chemical reactions involving the transition of electrons will produce enough energy to produce a UV (100nm) or a visible photon (400-700nm). </li></ul><ul><li>Nuclear reactions involving the formation of a nucleus will produce enough energy to produce a gamma ray photon (.00004nm). </li></ul>
  38. 38. BINDING ENERGY PER NUCLEON <ul><li>As mass number increases for stable nuclei, so does the binding energy. </li></ul><ul><li>By determining the average binding energy per nucleon (E b /A), the average energies for various nuclei can be compared directly. </li></ul>
  39. 39. BINDING ENERGY PER NUCLEON <ul><li>In a previous example, we found the total binding energy for the helium nucleus to be 28.3 MeV. </li></ul><ul><li>This means the average binding energy is 28.3/4 = 7.1 MeV. This means on average, 7.1 MeV of energy is needed to remove one nucleon. </li></ul>
  40. 40. BINDING ENERGY PER NUCLEON <ul><li>In the graph below, note the shape. </li></ul><ul><li>The value of E b /A rises rapidly with increasing A and then flattens off to an almost constant value. </li></ul><ul><li>Almost all of the nuclei have values between 7.3 and 8.8 MeV. </li></ul>
  42. 42. BINDING ENERGY PER NUCLEON <ul><li>Careful inspection shows that the maximum value occurs at 26 Fe 56 and slowly decreases. </li></ul><ul><li>This shows that iron has the most stable nucleus of all nuclei in the graph (takes the most energy to pry away a nucleon). </li></ul><ul><li>The curve can also be used to explain the production of energy from nuclear reactions that are covered below. </li></ul>
  43. 43. BINDING ENERGY PER NUCLEON <ul><li>If the graph is drawn for the light elements, peaks can be seen. </li></ul>
  44. 44. BINDING ENERGY PER NUCLEON <ul><li>The peaks occur for nuclei whose mass number is divisible by four: He-4, Be-8, C-12, O-16, Ne-20 and Mg-24. </li></ul><ul><li>This indicates how stable alpha particles ( 2 He 4 ) are. The peaks also indicate the existence of shells within the nucleus that are similar to the shells of the electrons in orbit. </li></ul>
  45. 45. EXAMPLE 2 <ul><li>Using the graph shown below, explain why the nucleus 26 Fe 56 is more stable than the nucleus 1 H 2 . </li></ul>
  46. 46. EXAMPLE 2 SOLUTION <ul><li>By inspection, 26 Fe 56 has a higher binding energy per nucleon than 1 H 2 . This means that there is a greater mass defect for the iron nucleus when compared to the heavy hydrogen nucleus. So, to remove a nucleon from each nucleus, more mass needs to be replaced for iron. This will require more energy, so the iron nucleus is more stable. </li></ul>
  47. 47. PARTICLE MASSES <ul><li>Energy can be converted over time from one form to another such as heat, light, kinetic etc. </li></ul><ul><li>Einstein showed that mass could be converted to energy and vice -versa using E = mc 2 . </li></ul>
  48. 48. PARTICLE MASSES <ul><li>Mass particles can be expressed in terms of their equivalent energies. </li></ul><ul><li>A proton has energy of 1.50 x 10 -10 J or 939 MeV. </li></ul><ul><li>The ‘mass’ of an electron is 0.511 MeV. </li></ul>
  49. 49. PARTICLE MASSES <ul><li>This energy is useful in calculations involving collisions between particles. </li></ul><ul><li>The initial kinetic energies of the particles and their masses is simply the total initial energy of the system. </li></ul>
  50. 50. CONSERVATION LAWS IN NUCLEAR REACTIONS <ul><li>In all interactions in nature, certain quantities are always conserved such as charge. </li></ul><ul><li>Example: </li></ul><ul><li>2 He + 7 N  8 O + 1 H </li></ul><ul><li>There are 9 positive charges on each side of the equation. </li></ul>
  51. 51. CONSERVATION LAWS IN NUCLEAR REACTIONS <ul><ul><li> This leads to the conservation of atomic number as the atomic number refers to the number of protons. </li></ul></ul><ul><ul><li> Mass number is also conserved. The individual nucleons may be converted from one type to another but the total number will remain constant. </li></ul></ul><ul><ul><li>Example: </li></ul></ul><ul><ul><li>He 4 + N 14  O 17 + H 1 </li></ul></ul>
  52. 52. CONSERVATION LAWS IN NUCLEAR REACTIONS <ul><ul><li> Linear and angular momentum are also conserved as they are isolated systems. </li></ul></ul>
  53. 53. CONSERVATION LAWS IN NUCLEAR REACTIONS <ul><ul><li> The total amount of mass and energy is conserved. It may be converted from one form to another, i.e. mass to energy by E =  mc 2 . </li></ul></ul><ul><ul><li>The mass of the elements in a nuclear reaction is always greater than the products. This has already been covered earlier. </li></ul></ul>
  54. 54. EXOTHERMIC NUCLEAR REACTIONS <ul><li>EXOTHERMIC NUCLEAR REACTIONS - give off energy. </li></ul><ul><li>1 H 2 = 3.3445 x 10 -27 kg </li></ul><ul><li>7 N 14 = 2.3252 x 10 -26 kg </li></ul><ul><li>6 C 12 = 1.9926 x 10 -26 kg </li></ul><ul><li>2 He 4 = 6.644 x 10 -27 kg </li></ul>
  55. 55. EXOTHERMIC NUCLEAR REACTIONS <ul><li>2.65965 x 10 -26 kg  2.657 x 10 -26 kg </li></ul><ul><li>Lost 2.65 x 10 -29 kg of mass </li></ul>
  56. 56. EXOTHERMIC NUCLEAR REACTIONS <ul><li>E = mc 2 </li></ul><ul><li>E = (2.65 x 10 -29 )(3 x 10 8 ) 2 </li></ul><ul><li>E = 2.385 x 10 -12 J </li></ul><ul><li>E = 1.49 x 10 7 eV </li></ul><ul><li>E = 14.9 MeV (Exothermic – energy given out) </li></ul>
  57. 57. ENDOTHERMIC NUCLEAR REACTION <ul><li>ENDOTHERMIC NUCLEAR REACTION- Incoming particles must have enough K to produce a nuclear reaction. </li></ul><ul><li>2 He 4 = 6.644 x 10 -27 kg </li></ul><ul><li>7 N 14 = 2.3252 x 10 -26 kg </li></ul><ul><li>8 O 17 = 2.8227 x 10 -26 kg </li></ul><ul><li>1 H 1 = 1.673 x 10 -27 kg </li></ul>
  58. 58. ENDOTHERMIC NUCLEAR REACTION <ul><li>2.9896 x 10 -26 kg  2.99 x 10 -26 kg </li></ul><ul><li>Gain of 4.0 x 10 -30 kg of mass </li></ul><ul><li>E = mc 2 </li></ul><ul><li>E = 3.6 x 10 -13 J </li></ul><ul><li>E = 2.25 x 10 6 eV </li></ul><ul><li>E = 2.25 MeV of Kinetic Energy required by the incoming particles to produce the nuclear reaction. </li></ul>
  59. 59. EXAMPLE 3 <ul><li>Complete the following nuclear reaction: </li></ul>
  61. 61. Conservation of Momentum <ul><li>In all interactions, the total momentum before the interaction is equal to the total momentum after the interaction. </li></ul><ul><li>This is also true for nuclear interactions. </li></ul>
  62. 62. Conservation of Momentum <ul><li>If a particle radioactively decays, its initial momentum before it decays is zero. This means the total momentum after the decay is also zero. As momentum is a vector quantity, we must consider both magnitude and direction. </li></ul>
  63. 63. Conservation of Momentum <ul><li>Thorium 90 Th 230 decays to an isotope of Radium 88 Ra 226 </li></ul><ul><li>And also emits a helium nucleus 2 He 4 . The formula for this reaction is: </li></ul><ul><li>Notice that the mass number and the atomic number is conserved. </li></ul>
  64. 64. Conservation of Momentum <ul><li>Consider the direction that the products will move off at after the decay. </li></ul><ul><li>The only way that momentum can be conserved is for them to move off in opposite directions. </li></ul><ul><li>This is because the total final momentum must equal zero. </li></ul>
  65. 65. Conservation of Momentum <ul><li>As the mass of the two particles is very different, so will the velocities. This is because the total momentum must equal zero ( p = m v ). </li></ul>
  66. 66. Conservation of Momentum <ul><li>To study the momentum in more detail, as the initial momentum is zero, we can say: </li></ul><ul><li>m Ra v f Ra = m He v f He </li></ul>
  67. 67. Conservation of Momentum <ul><li>This indicates that the helium nucleus will move away with a velocity 56.5 times that of the radium nucleus. </li></ul><ul><li>This is of course an approximation as mass has been lost in this reaction due to E = mc 2 . </li></ul>
  68. 68. Conservation of Momentum <ul><li>Originally, kinetic energy is also equal to zero. </li></ul><ul><li>After the decay, the kinetic is a value much more than zero. </li></ul><ul><li>This is because mass has been converted to energy. </li></ul>
  69. 69. Conservation of Momentum <ul><li>The ratio of kinetic energies are shown below: </li></ul>
  70. 70. Conservation of Momentum <ul><li>As a general rule, the particle with the smaller mass has the greater kinetic energy. </li></ul><ul><li>If a particle, such as an electron is ejected, it will have a much higher kinetic energy, as its mass is much smaller. </li></ul>
  71. 71. Conservation of Momentum <ul><li>The above process is called alpha decay as the Helium nucleus, being of smaller mass, will have the greatest kinetic energy and move off at the highest speed. </li></ul>
  72. 72. APP - PRODUCTION OF MEDICAL RADIOISOTOPES <ul><li>An atom can be changed from one type to another by the absorption or emission of a photon. </li></ul><ul><li>A nucleus can also be changed from one type to another by the absorption or emission of a proton or neutron. </li></ul>
  73. 73. APP - PRODUCTION OF MEDICAL RADIOISOTOPES <ul><li>The emission of protons or neutrons occurs naturally in radioactive material or in the bombardment of atmospheric gases by high-energy particles from space. </li></ul><ul><li>Artificially, radioisotopes are produced in one of two ways: </li></ul>
  74. 74. APP - PRODUCTION OF MEDICAL RADIOISOTOPES <ul><li> Nuclear Reactor </li></ul><ul><li>Nuclear Fission produces many radioisotopes in small quantities. </li></ul><ul><li>Stable isotopes are introduced and bombarding them with the many neutrons that are a part of the nuclear reactions. </li></ul><ul><li>The unstable nucleus can absorb the neutron and form a radioactive isotope of the same element or eject a proton and form a radioisotope of a different element. </li></ul>
  75. 75. APP - PRODUCTION OF MEDICAL RADIOISOTOPES <ul><li> Cyclotron </li></ul><ul><ul><li>or other particle accelerator </li></ul></ul><ul><li>Charged particles such as protons or deuterons </li></ul><ul><ul><li>heavy hydrogen (deuterium) nucleus </li></ul></ul><ul><li>are accelerated in the cyclotron and directed towards a stable nucleus. </li></ul><ul><li>As protons are fired at stable nuclei, only isotopes of different elements are formed. </li></ul>
  76. 76. APP - PRODUCTION OF MEDICAL RADIOISOTOPES <ul><li>Neutrons </li></ul><ul><ul><li>produced from a fission reactor </li></ul></ul><ul><ul><ul><li>Why not a cyclotron? </li></ul></ul></ul><ul><ul><li>can react with 32 S </li></ul></ul><ul><ul><li>To form a useful therapeutic radionuclide medical isotope </li></ul></ul>
  77. 77. APP - PRODUCTION OF MEDICAL RADIOISOTOPES <ul><li>Used in the treatment of: </li></ul><ul><ul><li>polycythemia vera </li></ul></ul><ul><ul><ul><li>excess red blood cells </li></ul></ul></ul><ul><ul><li>chronic myelocytic leukaemia, </li></ul></ul><ul><ul><li>chronic lymphocytic leukaemia, </li></ul></ul><ul><ul><li>certain ovarian and prostate carcinomas, </li></ul></ul>
  78. 78. APP - PRODUCTION OF MEDICAL RADIOISOTOPES <ul><li>Also </li></ul><ul><ul><li>palliation of metastatic skeletal disease, </li></ul></ul><ul><ul><li>and treatment of metastatic intrapleural and intraperitoneal effusions. </li></ul></ul>
  79. 79. APP - PRODUCTION OF MEDICAL RADIOISOTOPES <ul><li>Is a beta emitter </li></ul><ul><li>Equation? </li></ul><ul><li>Described as a Radiopharmaceutical </li></ul>
  80. 80. Radiopharmaceutical <ul><li>A molecule that consists of a radioisotope tracer attached to a pharmaceutical. </li></ul><ul><li>After entering the body, the radio-labelled pharmaceutical will accumulate in a specific organ or tumour tissue. </li></ul>
  81. 81. Radiopharmaceutical <ul><li>The radioisotope attached to the targeting pharmaceutical </li></ul><ul><li>undergoes decay and produces </li></ul><ul><li>specific amounts of radiation </li></ul><ul><li>used to diagnose or treat human diseases and injuries. </li></ul>
  82. 82. Radiopharmaceutical <ul><li>The amount of radiopharmaceutical administered is carefully selected to ensure each patient’s safety. </li></ul><ul><li>Radioisotopes are an essential part of radiopharmaceuticals. </li></ul>
  83. 83. APP - PRODUCTION OF MEDICAL RADIOISOTOPES <ul><li>When protons are accelerated in a cyclotron at oxygen, a radioactive isotope of fluorine is produced along with a neutron. </li></ul><ul><li>Notice that the atomic numbers and the atomic masses balance. </li></ul>
  84. 84. APP - PRODUCTION OF MEDICAL RADIOISOTOPES <ul><li>Using a table of masses, we can calculate the energy released. </li></ul><ul><li>Mass of 1 H 1 atom = 0.167353 x 10 -26 kg </li></ul><ul><li>Mass of 8 O 18 atom = 2.9896606 x 10 -26 kg </li></ul><ul><li>Total mass reactants =3.1570136 x 10 -26 kg </li></ul><ul><li>Mass of 9 F 18 atom = 2.9899558 x 10 -26 kg </li></ul><ul><li>Mass of 0 n 1 atom = 1.665 x 10 -27 kg </li></ul><ul><li>Total mass products =3.1564558 x 10 -26 kg </li></ul>
  85. 85. APP - PRODUCTION OF MEDICAL RADIOISOTOPES <ul><li> m = </li></ul><ul><li>3.1570136 x 10 -26 -3.1564558x 10 -26 </li></ul><ul><li> m = 0.0005578 x 10 -26 kg </li></ul><ul><li>E=  mc 2 = </li></ul><ul><li>5.578 x 10 -30 x (2.998 x 10 8 ) 2 </li></ul><ul><li>E = 5.0135 x 10 -13 J </li></ul><ul><li>E = 3.133 MeV </li></ul>
  86. 86. APP - PRODUCTION OF MEDICAL RADIOISOTOPES <ul><li>We are not making mass </li></ul><ul><li>Why is energy required for reaction to occur? </li></ul><ul><li>Conservation of momentum and energy </li></ul><ul><li>How much energy is required? </li></ul>
  87. 87. APP - PRODUCTION OF MEDICAL RADIOISOTOPES <ul><li>Minimum energy will produce fluorine and a neutron but they will be at rest. </li></ul><ul><li>As the proton was moving to begin with, this energy will not allow for the conservation of momentum. </li></ul>
  88. 88. APP - PRODUCTION OF MEDICAL RADIOISOTOPES <ul><li>Through a derivation outside this course, the minimum kinetic energy required for a particle striking a stationary nucleus is: </li></ul><ul><li>  </li></ul><ul><li>K min = (1 + m / M )  E  </li></ul><ul><li>  </li></ul><ul><li>Where m is the mass of the incoming particle and M is the mass of the stationary target. </li></ul>
  89. 89. APP - PRODUCTION OF MEDICAL RADIOISOTOPES <ul><li>Therefore the binding energy required for the nuclear reaction of the Hydrogen and Oxygen atom to occur will be… </li></ul><ul><li>= 3.308 MeV </li></ul>
  90. 90. APP - PRODUCTION OF MEDICAL RADIOISOTOPES <ul><li>This amount of energy (3.308 MeV) is higher than previously calculated ( 3.133 MeV) as some additional energy is required to get the process started. </li></ul>
  91. 91. APP - PRODUCTION OF MEDICAL RADIOISOTOPES <ul><li>15 O is produced by firing a deuteron at 14 N </li></ul><ul><li>Equations is? </li></ul>
  92. 92. APP - PRODUCTION OF MEDICAL RADIOISOTOPES <ul><li>Determine binding energy of reactants and products. </li></ul><ul><li>Determine mass defect </li></ul><ul><li>Determine energy </li></ul>
  93. 93. APP - PRODUCTION OF MEDICAL RADIOISOTOPES <ul><li>18 F and 15 O are used in PET scans, </li></ul><ul><li>Will study this in more detail in the next topic </li></ul>
  94. 94. FORMATION OF C 14 IN THE ATMOSPHERE <ul><li>As the neutrons collide with other nuclei, they transfer energy without reacting, eventually slowing down sufficiently to be absorbed. </li></ul><ul><li>The molecules then become incorporated into the molecules of CO 2 and are absorbed into the food chain. This forms the basis for carbon dating. </li></ul>
  95. 95. NITROGEN 13 PRODUCTION IN MEDICINE <ul><li>This is an example of how a radioactive isotope can be produced naturally. </li></ul><ul><li>It forms the basis for Positron Emission Tomography (PET), which shows the body’s anatomy or structure. PET images can be used to show aspects of body metabolism or function. </li></ul>
  96. 96. NITROGEN 13 PRODUCTION IN MEDICINE <ul><li>7 N 13 is produced in hospitals using cyclotrons. One way it is produced is shown below: </li></ul><ul><li>The energy released is negative (-0.281 MeV) in this reaction implying that the cyclotron must accelerate the deuterium ( 1 H 2 ) nucleus. </li></ul>
  97. 97. NITROGEN 13 PRODUCTION IN MEDICINE <ul><li>The other method discussed previously is the method is preferred by hospitals. </li></ul><ul><li>Although more energy is required, there is a greater abundance of 1 H 1 than deuterium. </li></ul>