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Nuclear Binding, Radioactivity

Physics 102: Lecture 27. Nuclear Binding, Radioactivity. Today’s Lecture will cover 29.1 - 4. Make sure your grade book entries are correct Honors projects are due!. Coulomb force. proton. electron. proton. neutron. Very strong force.

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Nuclear Binding, Radioactivity

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  1. Physics 102: Lecture 27 Nuclear Binding, Radioactivity • Today’s Lecture will cover 29.1 - 4 • Make sure your grade book entries are correct • Honors projects are due! Physics 102: Lecture 27, Slide 1

  2. Coulomb force proton electron proton neutron Very strong force Binding energy ofdeuteron=or 2.2Mev!That’s around 200,000 times bigger! Strong Nuclear Force Hydrogen atom:Binding energy=13.6eV (of electron to nucleus) Simplest Nucleus: Deuteron=neutron+proton Physics 102: Lecture 27, Slide 2

  3. Hydrogen Atom: Bohr radius = Example has radius Nucleus with nucl number A: A Note the TREMENDOUS difference Z Smaller is Bigger! ComparingNuclearandAtomicsizes Nucleus is 104 times smaller and binding energy is 105 times larger! Physics 102: Lecture 27, Slide 3

  4. Preflight 27.2 Where does the energy released in the nuclear reactions of the sun come from? • covalent bonds between atoms • binding energy of electrons to the nucleus • (3) binding energy of nucleons Physics 102: Lecture 27, Slide 4

  5. Preflight 27.2 Where does the energy released in the nuclear reactions of the sun come from? • covalent bonds between atoms • binding energy of electrons to the nucleus • (3) binding energy of nucleons Physics 102: Lecture 27, Slide 5

  6. Proton: mc2 = 938.3MeV Adding these, get 1877.8MeV Neutron:mc2= 939.5MeV Binding Energy Einstein’s famous equation E = m c2 Example Difference is Binding energy,2.2MeV Deuteron: mc2 =1875.6MeV Physics 102: Lecture 27, Slide 6

  7. Proton: mc2 = 938.3MeV Adding these, get 1877.8MeV Neutron:mc2= 939.5MeV Binding Energy Einstein’s famous equation E = m c2 Example Difference is Binding energy,2.2MeV Deuteron: mc2 =1875.6MeV MDeuteron = MProton + MNeutron – |Binding Energy| Physics 102: Lecture 27, Slide 7

  8. Binding Energy Plot Iron (Fe) is most binding energy/nucleon. Lighter have too few nucleons, heavier have too many. 10 BINDING ENERGY in MeV/nucleon Fission = Breaking large atoms into small Fusion = Combining small atoms into large Physics 102: Lecture 27, Slide 8

  9. Fusion Binding Energy Plot Iron (Fe) is most binding energy/nucleon. Lighter have too few nucleons, heavier have too many. 10 Fission BINDING ENERGY in MeV/nucleon Fission = Breaking large atoms into small Fusion = Combining small atoms into large Physics 102: Lecture 27, Slide 9

  10. Preflight 27.3 Which element has the highest binding energy/nucleon? • Neon (Z=10) • Iron (Z=26) • Iodine (Z=53) Physics 102: Lecture 27, Slide 10

  11. Preflight 27.3 Which element has the highest binding energy/nucleon? • Neon (Z=10) • Iron (Z=26) • Iodine (Z=53) Physics 102: Lecture 27, Slide 11

  12. Preflight 27.4 Which of the following is most correct for the total binding energy of an Iron atom (Z=26)? 9 MeV 234 MeV 270 MeV 504 Mev Physics 102: Lecture 27, Slide 12

  13. has 56 nucleons Preflight 27.4 Which of the following is most correct for the total binding energy of an Iron atom (Z=26)? 9 MeV 234 MeV 270 MeV 504 Mev For Fe, B.E./nucleon 9MeV Total B.E  56x9=504 MeV Physics 102: Lecture 27, Slide 13

  14. a particles: nucleii 3 Types of Radioactivity B field into screen Radioactive sources detector Easily Stopped b- particles: electrons Stopped by metal g : photons (more energetic than x-rays)penetrate! Physics 102: Lecture 27, Slide 14

  15. Example Decay Rules • Nucleon Number is conserved. • Atomic Number (charge) is conserved. • Energy and momentum are conserved. :example recall • 238 = 234 + 4 Nucleon number conserved • 92 = 90 + 2 Charge conserved :example Needed to conserve energy and momentum. g:example Physics 102: Lecture 27, Slide 15

  16. Preflight 27.6 A nucleus undergoes  decay. Which of the following is FALSE? 1. Nucleon number decreases by 4 2. Neutron number decreases by 2 3. Charge on nucleus increases by 2 Physics 102: Lecture 27, Slide 16

  17.  decay is the emission of A decreases by 4 Z decreases by 2 (charge decreases!) Preflight 27.6 A nucleus undergoes  decay. Which of the following is FALSE? • Nucleon number decreases by 4 • 2. Neutron number decreases by 2 • 3. Charge on nucleus increases by 2 Ex. Physics 102: Lecture 27, Slide 17

  18. The nucleus undergoes decay. Which of the following is true? 1. The number of protons in the daughter nucleus increases by one. 2. The number of neutrons in the daughter nucleus increases by one. Preflight 27.7 Physics 102: Lecture 27, Slide 18

  19. The nucleus undergoes decay. Which of the following is true? 1. The number of protons in the daughter nucleus increases by one. 2. The number of neutrons in the daughter nucleus increases by one. decay is accompanied by the emission of an electron: creation of a charge -e. In fact, inside the nucleus, and the electron and neutrino “escape.” Preflight 27.7

  20. ACT: Decay Which of the following decays is NOT allowed? 1 2 3 4 Physics 102: Lecture 27, Slide 20

  21. 238 = 234 + 4 92 = 90 + 2 214 = 210 + 4 84 = 82 + 2 14 = 14+0 6 <> 7+0 40 = 40+0+0 19 = 20-1+0 ACT: Decay Which of the following decays is NOT allowed? 1 2 3 4 Physics 102: Lecture 27, Slide 21

  22. No. of nuclei present Decays per second, or “activity” decay constant Preflight 27.8 If the number of radioactive nuclei present is cut in half, how does the activity change? 1 It remains the same 2 It is cut in half 3 It doubles Physics 102: Lecture 27, Slide 22

  23. No. of nuclei present Decays per second, or “activity” decay constant Preflight 27.8 If the number of radioactive nuclei present is cut in half, how does the activity change? 1 It remains the same 2 It is cut in half 3 It doubles Physics 102: Lecture 27, Slide 23

  24. No. of nuclei present Decays per second, or “activity” decay constant ACT: Radioactivity Start with 16 14C atoms. After 6000 years, there are only 8 left. How many will be left after another 6000 years? 1) 0 2) 4 3) 8 Physics 102: Lecture 27, Slide 24

  25. No. of nuclei present Decays per second, or “activity” decay constant ACT: Radioactivity Start with 16 14C atoms. After 6000 years, there are only 8 left. How many will be left after another 6000 years? 1) 0 2) 4 3) 8 Every 6000 years ½ of atoms decay Physics 102: Lecture 27, Slide 25

  26. Decay Function time Physics 102: Lecture 27, Slide 26

  27. Preflight 27.9 The half-life for beta-decay of 14C is ~6,000 years. You test a fossil and find that only 25% of its 14C is un-decayed. How old is the fossil? 3,000 years 6,000 years 12,000 years Physics 102: Lecture 27, Slide 27

  28. At 6,000 years: 50% remains At 12,000 years: 25% remains Preflight 27.9 The half-life for beta-decay of 14C is ~6,000 years. You test a fossil and find that only 25% of its 14C is un-decayed. How old is the fossil? 3,000 years 6,000 years 12,000 years At 0 years: 100% remains Physics 102: Lecture 27, Slide 28

  29. Survival: No. of nuclei present at time t No. we started with at t=0 No. of nuclei present Decays per second, or “activity” decay constant where Half life Then we can write Radioactivity Quantitatively Instead of baseewe can use base2:

  30. Example You are radioactive! One in 8.3x1011 carbon atoms is 14C which b- decays with a ½ life of 5730 years. Determine # of decays/gram of Carbon. Physics 102: Lecture 27, Slide 30

  31. Example You are radioactive! One in 8.3x1011 carbon atoms is 14C which b- decays with a ½ life of 5730 years. Determine # of decays/gram of Carbon. Physics 102: Lecture 27, Slide 31

  32. Carbon Dating We just determined that living organisms should have a decay rate of about 0.23 decays/ gram of carbon. The bones of an ice man are found to have a decay rate of 0.115 decays/gram. We can estimate he died about 6000 years ago. Example Physics 102: Lecture 27, Slide 32

  33. ACT: Binding Energy • Which system “weighs” more? • Two balls attached by a relaxed spring. • Two balls attached by a stretched spring. • They have the same weight. Physics 102: Lecture 27, Slide 33

  34. ACT: Binding Energy • Which system “weighs” more? • Two balls attached by a relaxed spring. • Two balls attached by a stretched spring. • They have the same weight. M1 = Mballs + Mspring M2 = Mballs + Mspring + Espring/c2 M2 – M1 = Espring/c2 ≈ 10-16 Kg Physics 102: Lecture 27, Slide 34

  35. Strong Nuclear Force • Acts on Protons and Neutrons • Strong enough to overcome Coulomb repulsion • Acts over very short distances Two atoms don’t feel force Physics 102: Lecture 27, Slide 35

  36. Survival: Summary • Nuclear Reactions • Nucleon number conserved • Charge conserved • Energy/Momentum conserved • a particles = nucleii • b- particles = electrons • g particles = high-energy photons • Decays • Half-Life is time for ½ of atoms to decay Physics 102: Lecture 27, Slide 36

  37. See you next time! • Read Textbook Sections 26.1 – 26.7 • Take a look at Special Relativity in 14 Easy (Hyper)lessons: http://web.hep.uiuc.edu/home/g-gollin/relativity/ Finals Week office hours Will be posted on the web Physics 102: Lecture 27, Slide 37

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