Chapter 23.3_23.4 as handout

Chapter 23.3_23.4 as handout - Kinetics of Radioactive...

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1 Kinetics of Radioactive Decay N daughter rate = - Δ N Δ t rate = λ N Δ N Δ t = λ N - N = N 0 exp( - λ t ) or: ln N = lnN 0 - λ t N = the number of atoms at time t N 0 = the number of atoms at time t = 0 λ is the decay constant: ln2 = t ½ λ 23.3 equating: Kinetics of Radioactive Decay [N] = [N] 0 exp( - λ t ) ln[N] = ln[N] 0 - λ t [N] ln [N] 23.3 Radiocarbon Dating 14 N + 1 n 14 C + 1 H 7 1 6 0 14 C 14 N + 0 β + ν 6 7 -1 t ½ = 5730 years Uranium-238 Dating 238 U 206 Pb + 8 4 α + 6 0 β 92 -1 82 2 t ½ = 4.51 x 10 9 years 23.3
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2 Nuclear Transmutation Cyclotron Particle Accelerator 14 N + 4 α 17 O + 1 p 7 2 8 1 27 Al + 4 α 30 P + 1 n 13 2 15 0 14 N + 1 p 11 C + 4 α 7 1 6 2 23.4 Nuclear Transmutation 23.4 Nuclear Fission 23.5 235 U + 1 n 90 Sr + 143 Xe + 3 1 n + Energy 92 54 38 0 0 Energy = [mass 235 U + mass n – (mass 90 Sr + mass 143 Xe + 3 x mass n )] x c 2 Energy = 3.3 x 10 -11 J per 235 U = 2.0 x 10 13 J/mole 235 U Combustion of 1 ton of coal = 5 x 10 7 J = 8.4 x 10 10 J/g 235 U = 8.4 x 10 16 J/ton 235 U
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3 Nuclear Fission 23.5 235 U + 1 n 90 Sr + 143 Xe + 3 1 n + Energy 92 54 38 0 0 Representative fission reaction Nuclear Fission
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Chapter 23.3_23.4 as handout - Kinetics of Radioactive...

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