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# 04 chap 02 nuclear transformations

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### 04 chap 02 nuclear transformations

1. 1. Chapter 2Nuclear Transformations 1
2. 2. 2.1 RADIOACTIVITYFirst discovered by Becquerel in 1896, radioactivity is a phenomenon in whichradiation (α,β, or γ) is given off by the nuclei of the elements. Pierre and MarieCurie discovered radium and polonium in 1898. The Nobel Prize in Physics 1903 Henri Becquerel Pierre Curie Marie Curie (1852-1908) (1859-1906) (1867-1934) 2
3. 3. 2.1 RADIOACTIVITY (cont’d) Nucleons (protons, neutrons) in a nucleus possess kineticenergy. In a stable nucleus, this energy is insufficient topenetrate the potential barrier. In a radioactive nucleus, it hasexcess energy that is constantly redistributed among thenucleons by mutual collisions. As a matter of probability, one of the particles may gainenough energy to escape from the nucleus, leaving thenucleus in a lower energy state. The emission of a particlemay still leave the nucleus in an excited state, furtheremissions follow until the the nucleus is stable (ground state). 3
4. 4. 2.1 RADIOACTIVITY (cont’d) γ α A=4 magnetic field (++) applied β perpendicular to (-) the paper radium source 4
5. 5. 2.2 DECAY CONSTANTIn a large collection of atoms, the number of atoms thatwill decay (or disintegrate) per unit time is proportionalto the number of radioactive atoms present. λ is thedecay constant. ∆N ∝ N = - λN ∆t d N = - λN dt N = N0e-λt 5
6. 6. 2.3 ACTIVITYThe rate of decay dN/dt is called activity. A = - λN A = A0e-λtThe unit of activity is the curie (Ci), defined as:1 Ci = 3.7 × 1010 disintegration/sec (dps)Similarly, 1 mCi = 3.7 × 107 dps, and 1 µCi = 3.7 × 104 dps.The SI unit is becquerel (Bq):1 Bq = 1 dps = 2.70 × 10-11 Ci. 6
7. 7. 2.4 THE HALF-LIFE and THE MEAN LIFEThe half-life (T1/2) is the time required for the activity (or thenumber of radioactive atoms) to decay to half the initial value. N/N0 = A/A0 = ½ = e-λT1/2 ln 2 0.693 T1/2 = = λ λ The mean life or average life, Ta, is defined as: 1 Ta = = 1.44 T1/2 λ 7
8. 8. 100 100 90 ln(A) = -n ln(2) 80 = -0.693 n 70 A = (½)nActivity Remaining (%) 60 50 10 40 30 20 10 0 1 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Time (T1/2 Units) Time (T1/2 Units) 8
9. 9. Example 1• Calculate the number of atoms in 1 gram of 226Ra.Number of atoms/g = NA/AW = 6.02×1023/226 = 2.66×1021(b) What is the activity of 1 gram of 226Ra (T1/2 = 1622 years)A = λNλ = 0.693/ T1/2 = 0.693/(1622y × 365d/y × 86400sec/d) = 1.356 × 10-11/secA = 2.66×1021 × 1.356 × 10-11 dps/g = 3.61 × 1010 dps/g 9 = 0.975 Ci/g (specific activity)
10. 10. Example 2• Calculate the decay constant for 60Co (T1/2 = 5.26 years) in units of month-1.λ = 0.693/ T1/2T1/2 = 5.26 years = 63.12 monthsλ = 0.693/63.12 = 1.0979 × 10-2 /month(b) What will be the activity of a 5,000 Ci 60Co after 4 yearsA = A0e-λt = 5000 × e -1.0979 × 10-2 × 48 10 = 2952 Ci
11. 11. Example 3When will 5 mCi of 131I (T1/2 = 8.05 days) and 2 mCi of 32P (T1/2 = 14.3 days) have equal activities?For 131I : A0 = 5 mCi, λ = 0.693/8.05 = 8.609 × 10-2 /dayFor 32P : A0 = 2 mCi, λ = 0.693/14.3 = 4.846 × 10-2 /day 5 × e –8.609 × 10-2 × t = 2 × e –4.846 × 10-2 × t ln 5 – 8.609 × 10-2 × t = ln 2 – 4.846 × 10-2 × t t = 24.34 days 11
12. 12. 2.5 RADIOACTIVE SERIESNaturally occurred elements (Z = 1 to 92), artificial elements(Z = 93 to 103).Radioactive elements tend to have higher Z.Naturally occurred radioactive elements grouped into 3 series: α,β,(γ) 206Uranium series: 238 U (T1/2 = 4.51×10 years) 9 Pb α,β,(γ) 207Actinium series: 235U (T1/2 = 7.13×108 years) Pb α,β,(γ) 208Thorium series: 232 Th (T1/2 = 1.39×10 years) 10 Pb 12
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15. 15. 2.6 RADIOACTIVE EQUILIBRIUM decay, λ1 decay, λ2 parent nuclide daughter nuclide (radioactive) (radioactive) dN1  = −λ1 N1  dt dN 2   ⇒ A2 = A1 λ2 λ2 − λ1 [ 1 − e −( λ2 −λ1 ) t ] = λ1 N1 − λ2 N 2  dt   If the half-life of the parent > the half-life of the daughter, then after a certain period of time, a condition of equilibrium is achieved: A2/A1 = constant The apparent decay rate of the daughter is then governed by the half-life of the parent. 15
16. 16. 2.6 RADIOACTIVE EQUILIBRIUM (cont’d) 1.0 99 MoTransient equilibrium:T1/2 of the parent is not much 0.5longer than the T1/2 of the Tc 99mdaughter.99 Mo: T1/2 = 67 h99m Tc: T1/2 = 6 h 0.1 0 20 40 60 80 100 120 Time (hours) 16
17. 17. 2.6 RADIOACTIVE EQUILIBRIUM 1.0 226 RaSecular equilibrium:T1/2 of the parent is much 0.5 222 Rnlonger than the T1/2 of thedaughter.226 Ra: T1/2 = 1622 years222 Rn: T1/2 = 3.8 days A1 = A2 0.1 λ1N1 = λ2N2 0 5 10 15 20 25 30 Time (days) 17
18. 18. 2.7 MODES OF RADIOACTIVE DECAYα-particle decay: (nuclides with too many protons)• Radioactive nuclides with very high atomic numbers (greater than 82) decay most frequently with the emission of an a particle A A-4 4 Z X Z-2 Y + 2 He + Q 226 222 4 88 Ra 86 Rn + 2 He + 4.87 MeV Q appears almost entirely as kinetic energy of the α- particle, because Y is much heavier than the α-particle. 18
19. 19. 2.7 MODES OF RADIOACTIVE DECAY (cont’d) β-particle decay: A A 0 Negatron emission: Z X Z+1 Y + -1 β +υ+Q(nuclides with too many T1/2 32 32 0neutrons) 15 P 16 S + -1 β + υ + 1.7 MeV 14.3 days Eavg = 0.69 MeV ~ 1/3 Emax Emax = 1.71 MeV 19 β-particles are emitted with a spectrum of energies.
20. 20. 2.7 MODES OF RADIOACTIVE DECAY (cont’d) A A 0 Positron emission: Z X Z-1 Y ++1 β +υ+Q (nuclides with too few T1/2 22 22 0 neutrons) 11 Na 10 Ne ++1β + υ + 1.82 MeV 2.60 years 22 11 NaEnergy level T1/2 = 2.60 ydiagram for the β+(90%),Emax= 0.54 MeV (1.02 MeV)positron decay 22 22 EC(10%)of 11 Na to10 Ne β+(0.05%),Emax=1.83 MeV γ(1.27 MeV) 22 10 Ne 20
21. 21. 2.7 MODES OF RADIOACTIVE DECAY (cont’d) Electron capture: one of the orbital electrons is captured by the nucleus (when the nucleus has too few neutrons). 1 0 1 1 p + -1 e 0n + υ A 0 A Z X +-1 β Z-1 Y + υ + Q Outer-shell electron falls into the (inner-shell) hole createdMost likely a K-shell electron which may itself be absorbed by the captured electron,is captured, called K capture. and ejects an Auger electron. producing characteristic x- rays, 21
22. 22. 2.7 MODES OF RADIOACTIVE DECAY (cont’d)In most radioactive transformations, In internal conversion, one of the orbitalthe daughter nucleus loses the excess electrons is ejected from the atom,energy immediately in the forms of γ usually followed by characteristic x raysrays or by internal conversion. and auger electrons. (analogous to photo- electric effect)Isomeric transition: sometimes, the excited state of the daughter nucleuspersists for an appreciable time, called metastable state. This is the isomer ofthe final product nucleus. 22
23. 23. 2.8 NUCLEAR REACTIONS a + A → B + b + energy or A(a, b) BThe α,p reaction: The bombardment of a nucleus by αparticles with the subsequent emission of protons. A 4 A+3 1 Z X + 2 He Z+1 Y +1 H + Q A X (α,p) A+3Y Q>0: exoergic, energy is released Q<0: endoergic, energy is absorbed (to be supplied by the bombarding particle in the form of kinetic energy). Q is the difference in the masses of the initial & final particles. 14 4 17 1 7 N + 2 He 8O +1 H – 1.19 MeV 23
24. 24. 2.8 NUCLEAR REACTIONS (cont’d)The α,n reaction: The bombardment of a nucleus by αparticles with the subsequent emission of neutrons. A 4 A+3 1 Z X +2 He Z+2 Y +0 n +Q 9 Be (α,n) 12CProton bombardment: proton being captured by the nucleuswith the emission of γ rays. A 1 A+1 Z X +1 p Z+1 Y +Q 7 Li (p,γ) 8Be 24
25. 25. 2.8 NUCLEAR REACTIONS (cont’d)Deuteron bombardment: The bombardment of a nucleusby deuterons with the subsequent emission of neutrons orprotons. A X (d,n) A+1 Y A Z X (d,p) A+1 Y Z Z Z+1 2 9 10 1 1 H +4 Be 5B +0n 25
26. 26. 2.8 NUCLEAR REACTIONS (cont’d)neutron bombardment: neutrons are effective in producingnuclear reactions since they possess no electric charge. Inparticular, thermal neutrons (or slow neutrons, energy =0.025 eV) are very effective. 10 1 7 4(n,α) reaction: 5 B +0n 3 Li + 2 He (BNCT) 59 1 60 Co + n +γ (Production(n,γ) reaction: 27 0 27 Co of 60Co) 60 T1/2 60 0 27 Co 28 Ni + -1 β + γ1 + γ2 5.26 years 26
27. 27. 2.8 NUCLEAR REACTIONS (cont’d) 14 1 14 1(n,p) reaction: 7 N +0 n 6 C + 1H 14 T1/2 14 0 6 C 7N + -1 β 5700 years 32 1 32 1(n,p) reaction: 16 S + 0n 15 P + 1H 32 T1/2 32 0 15 P 16 S + -1 β 14.3 days 27
28. 28. 2.8 NUCLEAR REACTIONS (cont’d) 63 62 1Photo disintegration: 29 Cu +γ 29 Cu + 0 nfission:235 236 141 92 92 U + 1n 0 92 U 56 Ba + 36 Kr + 3 1n + Q 0 Q ~ 200 MeVfusion:2 41 H + 3H 1 2 He + 1n + Q 0 Q = 17.6 MeV 28
29. 29. 2.9 ACTIVATION OF NUCLIDESRadioactive elements can be made by various nuclearreactions.The yield of a nuclear reaction depends on the number ofbombarding particles, the number of target nuclei, and theprobability of the nuclear reaction, called cross-section,given in units of barns (10-24 cm2). 29
30. 30. 2.10 NUCLEAR REACTORSIn a nuclear reactor, self-sustaining chain reaction isachieved (called critical). High fluxes of thermal neutronsare produced (1010 to 1014 neutrons/sec/cm2).Neutrons are slowed down by colliding with low-Zmaterials, called ‘moderator’, such as water, graphite,beryllium.Radioisotopes such as 60Co are produced in nuclearreactors. 30