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Radioactivity Radioactivity is the spontaneous disintegration of an unstable nucleus. All spontaneous nuclear reactions are exothermic. Three types of radiation are alpha, beta, and gamma. 15 - 1 Alpha Radiation An alpha particle symbolized by α is the nucleus of a helium atom. Another way to symbolize an alpha particle is 4 He . 2 An example of alpha decay is given by the equation: 238U 92 234Th + 4 He 90 2 15 - 2 During alpha emission, the atomic number decreases by 2 and the mass number decreases by 4. Also indicated in the nuclear equation shown below is a conservation of mass-energy and charge. Mass number which is the number of nucleons. 238U 92 234Th + 4 He 90 2 Atomic number which is the number of protons. 15 - 3 Beta Particles A beta particle symbolized by β is a high speed electron. Another way to symbolize an beta particle is 0e. 1 An example of beta decay is given by the equation: 1n 0 1p + 0 e 1 1 15 - 4 During beta emission, the atomic number increases by 1 and the mass number remains the same. Also indicated in the nuclear equation shown below is a conservation of mass-energy and charge. Mass number which is the number of nucleons. 1n 0 1p + 0 e 1 1 Atomic number which is the number of protons. 15 - 5 Gamma Radiation A gamma particle symbolized by γ is a high energy photon. γ decay results from the redistribution of charge in the nucleus and accompanies most nuclear reactions. Because neither the mass number nor the atomic number changes during γ decay it is usually omitted from nuclear equations. 15 - 6 A particular decay series starts with U-238 followed by 4 emissions. The order of the emissions are an alpha, two beta, and another alpha decay. What are you left with after the 4th decay? 238U 92 234Th + 4 He 90 2 234Th 90 234U + 2 0e -1 92 234U 92 4 He + 230Th 2 90 15 - 7 Half-Life a Measure of Nuclear Activity The half-life of a radioisotope (a radioactive isotope) is the time necessary for one-half of the atoms/nuclei to decay. The rate of decay is independent of environmental conditions such as pressure and temperature. Although the half-life remains the same, the number of nuclei decreases as a function of time. 15 - 8 The rate of decay is given by Rate = kN where k is the rate or decay constant in units of /s, /y, etc. and N is the number of atoms (nuclei) in the sample. Rates are measure in unit of becquerel (Bq) which equals 1 disintegration/s. A decay series come to an end when the product is stable (no longer radioactive). 15 - 9 Because the rate of decay is a first-order kinetics process, the half-life is given by: t1/2 0.693 = k and the integrated rate law is given by: N m ln = -kt = ln m0 N0 where N and N0 are numbers of atoms or nuclei and m and m0 are masses in the same units. 15 - 10 Graph of Decaying Isotope vs Time The graph shown on the next slide is Mass of Decaying Isotope vs Time. The graph shows two important points: Nuclear decay is an example of first-order kinetics which means the half-life remains constant which is 60 days. As a radioactive substance decays, the amount of radiation decays as well. 15 - 11 Mass of Decaying Isotope vs Time Mass Of Decaying Isotope (mg) Mass Of Decaying Isotope vs Time 120.0 100.0 80.0 1 half-life (60 days, 50.0 g) 2 half-lives (120 days, 25 g) 60.0 40.0 20.0 0.0 0 100 200 300 400 500 600 Time (days) 15 - 12 Bi-210 has a half-life of 5.0 days. Approximately would it take for 12.5% of a 2.00 mg sample of this radioisotope to decay? t1/2 = 5.0 d m0 = 2.00 mg t1/2 0.693 = k 0.693 k= 5.0 ln m = -kt m0 15 - 13 . 0.693 0.875 × 2.00 mg ln t = 2.00 mg 5.0 t = 0.96 days 15 - 14 Nuclear Stability Atomic nuclei consist of positively charged protons and neutrons that are neutral. According to the law of electrostatics, protons should repel each other and all nuclei should disintegrate. However, at very short distances of approximately 10-15 m, a strong nuclear force (a strong attractive force) exists between nucleons (protons and neutrons). 15 - 15 The more protons that are packed in the small dense nucleus, the more neutrons are needed to provide the “nuclear glue”. The graph on the next slide shows that the lighter elements (up to about 20) have approximately equal numbers of protons and neutrons. However, the number of neutrons needed for stability increases more rapidly than the number of protons. 15 - 16 Neutron Number vs Proton Number Number Of Neutrons vs Number Of Protons Number Of Neutrons (A - Z) 82Pb 160 50Sn 140 (1.52:1) (1.38:1) 120 Too many neutrons 100 80 1:1 6C (1:1) 60 40 Too many protons 20 0 0 20 40 60 80 100 Number Of Protons (Z) 15 - 17 The blue graph shows the nuclei that do not decay. The stable nuclei are said to reside in the “belt of stability”. As the number of protons in the nucleus increases, the ratio of neutrons to protons also increases to provide nuclear stability. 15 - 18 Rules for Nuclear Stability The neutron to proton ratio required for nuclear stability varies with atomic number. For the lighter elements (up to about 20), the ratio is close to 1:1 as indicated by both the red and blue graph segments. As the atomic number increases beyond 20, the ratio of neutrons to protons increase as indicated by the blue graph segment. 15 - 19 All elements beyond Bi-83 are radioactive. Nuclei with an even number of nucleons are more stable than those with an odd number of nucleons. The unstable region resulting from the nucleus having too many neutrons (above the blue segment) undergoes spontaneous beta decay to become more stable. 15 - 20 The unstable region resulting from a nucleus with too many protons (below the red segment) undergoes spontaneous positron decay or electron capture to become more stable. For the lighter nuclei nuclei, positron emission is favored and for the heavier nuclei, electron capture is favored. Electron capture occurs when a nucleus absorbs an innermost electron (n = 1) to form a neutron. 15 - 21 1p + 0 e 1 1 1n 0 There are certain numbers of protons and neutrons that produce very stable nuclei. These numbers are referred to magic numbers and are 2, 8, 20, 28, 50, 82, and 126. 15 - 22 Which pair of nuclei is more stable? 1) 6 Li or 9 Li 3 3 6Li is more stable because as a light element, 3 a 1 proton : 1 neutron is required. Pb or 209At 2) 204 82 85 204Pb is more stable because all elements 82 with Z > 83 are unstable. 15 - 23 Nuclear Binding Energy It is always true that a nucleus has less mass than the sum of its constituent particles. This difference in mass is called the mass defect. The mass defect can be used to calculate the nuclear binding energy given by: ΔE = Δmc2 15 - 24 where m is the mass in kilograms (kg), c is the speed of light, 3.0 x 108m/s, and E is the binding energy in joules (J). The greater the binding energy/nucleon, the more stable the nucleus. The energy equivalent of the mass defect is transformed into the kinetic energy of the particles. 15 - 25 When a lithium nucleus collides with a proton, two helium nuclei are formed each having a mass of 4.0015 u. Using the given information below, determine the amount of energy released in this transmutation. mLi = 7.0144 u mp = 1.0073 u mHe = 4.0015 u 7Li + 1H 3 1 1 amu = 1u = 931 MeV 4 2 2 He + energy 15 - 26 Δm = mr – mp Δm = 7.0144 u + 1.0073 u – 2 × 4.0015 u Δm = 0.0187 u 931 MeV E = Δm = 0.0187 u × 1u E = 17.4 MeV 15 - 27