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Nuclear Stability & Radioactive Decay

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Notation for a nuclide (specific atom) 12 C 6 The left superscript is the mass number = number of protons + neutrons.The left superscript is the mass number = number of protons + neutrons. The left subscript is the atomic number = number of protons.The left subscript is the atomic number = number of protons.

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Isotopes Atoms with identical atomic numbers but different mass numbers. (Two nuclides can have different atomic numbers and different mass numbers.)

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Nuclear Stability Determined by neutron/proton ratio. –All nuclides with 84 or more protons are unstable. –Light elements (up to atomic number 20): like a neutron/proton ratio of 1. –For heavier elements, the neutron/proton ratio required for stability > 1, and increases as atomic number increases. –Of 2000 known nuclides, only 279 are stable with respect to radioactive decay.

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Zone of Stability Beta decay Positron emission or electron capture Alpha decay: heavy elements.

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Radioactive Decay Represented by equations 14 C 14 N + 0 e 67 Original nuclide Decay Mode Decay Product

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Decay Modes Alpha – common decay mode for heavy nuclides. Mass # by 4, atomic # by 2. Tends to slightly increase n/p ratio. Beta – mass # remains constant. –Net effect: neutron changed to proton. So this is a likely decay mode for nuclides whose n/p ratio is too high – decreases n/p ratio.

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Decay Modes Positron production: net effect: change a proton to a neutron. –Important decay mode for nuclides whose n/p ratio is low – it increases the n/p ratio! Electron capture: inner-orbital electron is captured by the nucleus –Increases neutron-proton ratio

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Decay series Some radioactive nuclides must go through several decay events to reach a stable (nonradioactive) state. 235 U 207 Pb 238 U 206 Pb 9282 9282

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Kinetics of Radioactive Decay Can never predict exactly when a specific nuclide will decay. N = # of nuclides Rate = - ( N/ t) = kN i.e., the rate is directly proportional to the # of nuclides in the sample.

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Rate = - ( N/ t) = kN ln(N/N 0 ) = -kt N = # of nuclides remaining at time t N 0 = # of nuclides at t = 0.

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Half-Life, t ½ Half-life of a sample = time required for the number of nuclides to reach half the original value, N 0 /2. t ½ = 0.693/k

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Nuclear Transformations Change of one nuclide into another Target nucleus is bombarded by a “bullet” “Bullet” may be a positive ion or a neutron –Particle accelerators used for + ions –Positive ions must be accelerated to high KE to overcome electrostatic repulsions Cyclotron –Neutrons quite different experimentally. Not repelled by target nuclei.

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Transuranium Elements Elements 93 – 1** have been synthesized.

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Uses of Radioisotopes Ratioactive Dating 14 C 0 e + 14 N 67 Continuously produced in atm by: 14 N + 1 n 14 C + 1 H 7061 So, C-14 is incorporated into living plants. As long as it is alive, C-14 to C-12 ratio is constant. When plant dies, 14 C/ 12 C ratio starts to decrease. t ½ = 5730 yrs

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Geologic History 238 U 206 Pb 9282

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Medical Applications Radiotracers/Diagnosis –Radioactive nuclide whose pathway in an organism can be traced by monitoring its radioactivity. –I-131 thyroid –Th-201 heart Treatment

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Thermodynamic Stability of Nucleus Mass of a nucleus is always less than the sum of the masses of the protons and neutrons that make up the nucleus. This difference is a measure of the binding energy Binding energy = energy released when nucleus is formed.

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Chemical Potential Well Potential Energy Separate Nucleons Stable Nucleus Green Arrow represents binding energy: Energy RELEASED when nucleus is formed.

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Mass Defect for O-16 8p: (8 X 1.007276 amu) = 8.058208 amu 8n: (8 X 1.008665 amu) = 8.06932 amu 8e: (8 X 0.0005486 amu) = 0.004389 amu Total combined mass = 16.125789 Atomic mass of 0-16 = 15.994915 amu m = 0.130874 amu Use 1 amu = 1.66054 X 10 -27 kg

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Mass Defect for O-16 m = 0.130874 amu Use 1 amu = 1.66054 X 10 -27 kg m = 2.1732 X 10 -28 kg mc 2 = E = 1.9559 X 10 -11 kg m 2 s -2 E = 1.9559 X 10 -11 J per O-16 atom & 1.22 X 10 -12 J per nucleon In kJ/mol: 7.4 X 10 8 kJ per nucleon per mol

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Binding Energy/Nucleon vs. Mass #

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Units of binding energy Chemists use kJ/(mol nucleon) Physics uses a different unit: Mev

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Nuclear Fission Splitting a heavy nucleus into two smaller nuclei. U-235 and Pu-239 are fissionable fuels Reaction initiated by a neutron Many, many possible products

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Nuclear Fusion Two light nuclei combine to form a heavier, more stable nucleus. Occurs in the stars. Sun: 73% H, 26% He, and 1% other Protons fuse to form He

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Sun 1 H + 1 H 2 H + 0 e + energy 1 H + 2 H 3 He + energy Then 3 He + 3 He 4 He + 2 1 H + energy 3 He + 1 H 4 He + 0 e + energy 1111 112 2221 21 21

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Fusion vs. Fission as Energy Source

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Nuclear vs. Ordinary Chemical & Physical Change Nuclear transformations involve much larger energy changes than ordinary chemical & physical changes –Orders of magnitude larger

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Risks of radionuclides Somatic damage = damage to the organism itself, resulting in sickness or death Genetic damage = damage to genes

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