1. NE 301 - Introduction to Nuclear Science Spring 2012 Classroom Session 4: Radioactive Decay Types Radioactive Decay and Growth Isotopes and Decay Diagrams Nuclear Reactions Energy of nuclear reactions Neutron Cross Sections Activation Calculations

2. Reminder Load TurningPoint Reset slides Load List 2

3. The Energy Released (or consumed), Q Change in BE: Or since BE is related to mass defect Change in M: A + B  C + D +  E Preferred! because we have table B.1. Remember: The Equation Has to Be BALANCED!

4. Please remember… BALANCE! Before starting to work

5. 5 Main Radioactive Decay Modes (Table 5.1 -page 89-Shultis) Decay TypeDescriptionEmission Gamma (  ) Decay of excited nucleus Gamma photon alpha (  ) Alpha particle is emitted Alpha particle negatron (  - )n  p + +e - +  Electron and anti- neutrino positron (β + ) p +  n+e + + Positron and neutrino Electron Capture (EC) Orbital e - absorbed: p + +e -  n +  Neutrino proton (p)Proton ejectedProton neutron (n)Neutron ejectedNeutron Internal Conversion (IC) Electron (K-Shell) ejected*Electron Spontaneous Fission (sf) Fission fragments

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7. 7 Kinetic Energy of Radioactive Decay Products Parent nucleus is at rest (E th ~ 0.025 eV~17 o C) Conservation of Linear Momentum and Kinetic Energy requires products to travel in opposite directions (2 product). m 1 v 1 =m 2 v 2 Q=½ m 1 v 1 2 + ½ m 2 v 2 2 What is the energy of emitted particle? (it is what we measure) (it is what we measure) v1v1v1v1 m2m2m2m2 v2v2v2v2 m1m1m1m1 m1m1m1m1 m2m2m2m2 Original atom that will split in 2 pieces

8. 8 Kinematics of radioactive decay… Notice 2:1

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10. 10 Main Radioactive Decay Modes (Table 5.1 -page 89-Shultis) Decay TypeDescriptionEmission Gamma (  ) Decay of excited nucleus Gamma photon alpha (  ) Alpha particle is emitted Alpha particle negatron (  - )n  p + +e - +  Electron and anti- neutrino positron (β + ) p +  n+e + + Positron and neutrino Electron Capture (EC) Orbital e - absorbed: p + +e -  n +  Neutrino proton (p)Proton ejectedProton neutron (n)Neutron ejectedNeutron Internal Conversion (IC) Electron (K-Shell) ejected*Electron Spontaneous Fission (sf) Fission fragments

11. 11 Beta Decay Remember:  ’s DO NOT have exactly defined energies 3 body interactions Max energy = neutrino took zero energy away… What is this energy? Page 554

12. Page 98-Shultis  -,  + produce three products: Cannot say energy of  Neutrinos by Fermi (1933) We only can say maximum energy of 

13. Similarly for  ’s 13

14. 14 Kinetic Energy of De-excitation Decay Details of the decays are needed to predict the correct  spectrum. Radioactive Decay Diagrams (e.g. book) Write all 3 rxn shown In principle gamma (  ) photons would have Q of the reaction, but… Q=2.50 MeV Q=2.50 MeV

15. 15 Radioactive Decay Diagrams… In figure 5.4 Write all the reactions indicated in the diagram.

16. 16 Radioactive Decay Diagrams… In figure 5.6 Write all the reactions indicated in the diagram. If initially we have 100 g of 64 Cu, how much Zn and Ni will we have after all Cu has decayed?

17. 17 Branching Decay Example

18. 18 Branching Decay Example

19. On to 19

20. Binary Nuclear Reactions Binary = 2 reactants (many times 2 products too) Most important type of nuclear reaction Most elements produced by binary rxns. in stars Nomenclature: 20 Light nuclide usually projectile Heavy nuclide usually target Heavy Product Light Product

21. 21 Binary Reactions ( ,p) First reaction reported by Rutherford:  Nitrogen in air bombarded by alphas producing protons ( ,n) In 1932, the neutron was discovered (Chadwick).  Rxn. still used in some neutron generators today or or

22. 22 Example Binary Reactions, cont. ( ,n) Photo-nuclear rxns: Highly energetic gamma rays can knock neutrons out of the nucleus. (n,p) Fast neutrons react with oxygen in the water in a reactor core producing radioactive 16 N. or or or

23. Mechanisms of Nuclear Reactions Direct Interactions Projectiles w/ KE>40MeV have de Broglie wavelengths ~ size of a nucleon in target nucleus Usually interact with individual nucleons Near surface of nucleus (peripheral reactions) Compound Nucleus Projectiles w/ KE ~ MeV have de Broglie wavelengths ~ size of the whole target nucleus Usually interact with whole nucleus Forms compound, highly excited nucleus Products have no “memory” of the reactants. 23

24. Reaction Nomenclature: Transfer Reactions ( ,d) (d,n) Scattering Reactions (x,x) elastic (x,x’) inelastic Knockout Reactions (n,2n) (n,3n) (n,np) Capture (n,  ) Photo-Nuclear ( ,n) 24 Direct Reactions 1-2 nucleons transfer between projectile and target projectile and target remain the same (it is a collision) Direct Reaction: Original projectile emerges and is accompanied by other nucleons (i.e. spallation: SNS) Projectile is absorbed by target nucleus (usually leaving it excited) Strong gamma kicks nucleon from the target nucleus

25. 25 For Binary Reactions: x +X  Y + y x is a projectile with KE (E x ). X is a target stationary nucleus E X =0 simplification

26. 26 A 5.5 MeV  particle is incident on Li causing 7 Li( ,n) 10 B. What is the KE of neutron scattered 30 o ?

27. 27 1. 0 MeV 2. 0.31 MeV 3. 1.31 MeV 4. 2.31 MeV 5. 3.31 MeV 6. 5.5 MeV

28. 7 Li(alpha,n) 10 B 28 FIRST BALANCE THE EQUATION!!! Endothermic Rxn Neutron Energy = 1.31MeV What would be the neutron energy if incident alpha particle is 1MeV instead? Can’t happen…

29. Solution exists only if Potential “  ” Factors Q<0 Heavy projectiles ( m Y -m x <0 ) Large scattering angles Cos  <0 Big enough E x can guarantee Physical meaning: Threshold Energy Argument of root >0