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Chapter 19 Nuclear Chemistry Hill, Petrucci, McCreary & Perry 4th Ed. Radioactivity Spontaneous Nuclear Decay Alpha - α Beta - β Gamma - γ 4 2+ He 2 0 -1e 0γ 0 A Helium Cation ejected from . the nucleus at high energy. An electron ejected from the nucleus at high energy. . High Energy electromagnetic . radiation. Radioactivity Other Types of Nuclear Decay Positron emission: Beta(+) - β+ 0 +1e An anti-electron ejected from . the nucleus at high energy. Beta(+) - β+ 1 p 1 1n 0 + 0 +1e Beta decay - β 1n 0 1 p 1 + 0 -1 e Electron Capture - ec - A nucleus captures an electron from outside. 1 p 1 + 0 -1e 1n 0 . Nuclear Symbols Isotope Number ~ At. mass #n + #p = 235 92 U Atomic Number = #p = nuclear charge Elementary Particles: 1n 0 ; 0γ 0 ; 0 -1β Atomic Symbol 4 2+ He 2 0 or -1e ; ; 1 1H or 1p 1 0 or 0e β +1 +1 Balancing Nuclear Equations Alpha decay: Beta(+) decay: 226 88 Ra 95 43 + Tc Beta(-) decay: 14 6C Electron Capture 40 19 K 4 2+ He 2 0 +1 e + + + 0 -1 e 0 -1 e Can you balance these? The subscript numbers and the superscript numbers must be algebraically equal on each side of the arrow. Transmutation of Elements Nuclear Bombardment: . 14 N 7 9 4Be 14 7N + 1H 1 4 2+ He 2 + 1n 0 1n 0 + 1H 1 + 4 2+ He 2 + + Supply the missing nuclides! Neutrons are better particles to bombard the nucleus! Why? Nuclear Reactions Determine the missing Nuclide! Nuclear Fission: 1n 0 235 92U + + 94 Kr 36 + 3 10n Nuclear Fusion: 2 H 1 + 3 H 1 + Tritium "T" Deuterium "D" 1n 0 Nuclear Stability From the number of Stable Isotopes found in nature: Proton Numbers that are: Even Even Odd Neutron Numbers that are: Even Odd Even Odd Number of Isotopes: 157 52 50 Odd 5 Certain Even Numbers impart Special Stability: "Magic Numbers" Proton Numbers that have values of: 2, 8, 20, 28, 50, 82 [126] Neutron Numbers that have values of: 2, 8, 20, 28, 50, 82, 126 4 2He 16 8O 40 Ca 20 208 82 Pb Observations on Stability and Composition •Light nuclei up to calcium-40 have a n/p ratio near 1. Ca-40 n/p = 1,“double magic” •Heavier nuclei have correspondingly greater n/p ratios, Bi-209 heaviest stable nuclide has n/p = 126/83 = 1.52 •Heaviest nuclides decay by alpha decay, lose 4 mass units, slightly increases n/p. •Neutron rich nuclides, beta decay, n to p. •Proton rich nuclides, β+ or ec, p to n. Observations on Stability & Composition Binding Energy = ∆mc2 •The “most stable” nuclides have mass numbers between 55 & 60 = Fe through Ni •Light nuclei have the least binding energy per nucleon. Magic number effect strong. •Heaviest nuclei are less stable than mid range mass nuclei, per nucleon. Suggest reasons for energetic fusion and fission. Source of Nuclear Energy: E = ∆mc2 Matter is Converted into Energy E = ∆mc2 Joule = kg.m2/s2 One must use the "Exact Mass" of nucleons to calculate ∆m. ∆m = Σim(products) c = 3.00 x 10 8 m/s - Σjm(reactants) Where i & j are coefficients in the balanced nuclear equation and m is the "exact mass" of each nuclide in the equation. Notice the similarity to the Hess' Law equation for ∆H and ∆G. If ∆m is negative the reaction is exothermic ! Calculation of Nuclear Binding Energy Mass Defect = The mass loss on forming the Nuclide from Neutrons and Protons From: ∆m = Σim(products) - Σjm(reactants) This is actually mass loss in formation of a nuclide. Mass Defect = Exact Mass of Nuclide - Σim(neutrons) + Σjm(protons) Number of neutrons Number of protons, the "Atomic Number" To compare nuclide stability with another nuclide you need to divide each nuclide mass defect by the number of protons + neutrons. This gives the mass loss per nucleon. Each neutron and each proton is a constituent nucleon of a nuclide. Energetics of Nuclear Reactions See Section 19.7 p 812: E = mc2 1 u = 1.6606 x 10-27 kg A mass defect of 1 u (atomic mass unit) corresponds to 1.4924 x 10-10 Joule. 1 u => E = 931.5 MeV 1 MeV = 1.6022 x 10-13 Joule Binding Energy is defined as the energy to decompose a nuclide to neutrons and protons, its usually expressed in MeV. Calculating Binding Energy Calculate the mass defect and binding energy of 3 2 He Mass Defect = 3.01493 u = Exact Mass of Nuclide mp = 1.00728 u mn = 1.00867 u - Σim(neutrons) 3 2 He + Σjm(protons) Activity & Rates of Decay Rate of radioactive decay: A "first order" rate process A = λN rate = k[A]1 number of atoms activity, disentegrations/second decay constant A Unit of activity, the Curie, C 1 Ci i 3.7 x 1010 dis/s One Curie is the decay rate of 1 gram of Radium-226. Radionuclides are sold by activity: mCi and µCi Half-Life and the Activity Half-Life = Time required for half the atoms to decay: 0.693 t1 = 2 λ To calculate the activity and the decay constant: 0.693 λ = t1 2 convert to seconds Divide λ by 3.7 x 1010 s-1 to get the activity in Curies. Fraction of Nuclei Remaining and the Elapsed Time To Calculate the fraction of nuclei: Nt log N0 = -λt 2.303 = -0.301 t t1 2 To Calculate the elapsed time: N0 1 t t = 3.323 log 2 Nt To Calculate the "Age" of a sample, Infer the fraction from the Experimental Data and know the half-life or the activity. Radiocarbon Dating Based on the near constant levels of Carbon-14 in the Earth’s atmosphere formed by the reaction: 14 14 1 1 7N + n 0 6C + H 1 Constant Carbon-14 levels maintained by: Constant levels of nitrogen atoms in the atmosphere as N2. Constant levels of high energy neutrons from the sun. Radiocarbon Dating Calculate the age of a Jaw bone whose activity is 4.5 dis/s per gram of contained carbon if current activity levels are 15.3 dis/s per gram of contained carbon. The half-life of Carbon-14 is 5730 years. Infer the Carbon-14 fraction and calculate the elapsed time: t = 3.323 t 1 log N0 2 Nt