Nuclear Binding, Radioactivity

1. Physics 102: Lecture 27 Nuclear Binding, Radioactivity • Make sure your grade book entries are correct! • e.g. HOUR EXAMS, “EX” vs. “AB” • EX = excused, AB = absent = 0 credit • Honors projects are due May 3 • via email: Word/PDF, file name to include your full name • Please fill out on-line ICES forms

2. More important announcements • No discussion next week! (Disc. 13) • Lecture Wed. (May 5) will cover material • Bring “Physics 102 problem solver” • Come prepared! • Quiz (put in TA mailbox by Friday, May 7) • FINAL EXAM May 10 & 11 • Review session Sunday May 9, 3pm, 141 Loomis

3. 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

4. Deuterium Binding Energy 2.2 MeV ground state

5. Nuclei have energy level—just like atoms energy needed to remove a proton from 12C is 16.0 MeV energy needed to remove a neutron from 12C is 18.7 MeV 12C energy levels Note the energy scale is MeV rather than eV

6. 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! 13

7. Preflight 27.2 Where does the energy released in the nuclear reactions of the sun come from? • covalent bonds between atoms 17% • binding energy of electrons to the nucleus 36% • (3) binding energy of nucleons 47% 15

8. Proton: mc2 = 938.3MeV Adding these, get 1877.8MeV Neutron:mc2= 939.5MeV Binding Energy Einstein’s famous equation E = m c2 Example proton: mc2=(1.67x10-27kg)(3x108 m/s)2=1.50x10-10 J Difference is Binding energy,2.2MeV Deuteron: mc2 =1875.6MeV MDeuteron = MProton + MNeutron – |Binding Energy| 17

9. 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 19

10. Fusion Binding Energy Plot Iron (Fe) has 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 21

11. Preflight 27.3 Which element has the highest binding energy/nucleon? • Neon (Z=10) 31% • Iron (Z=26) 22% • Iodine (Z=53) 47% 22

12. has 56 nucleons Preflight 27.4 Which of the following is most correct for the total binding energy of an Iron atom (Z=26)? 13% 28% 31% 28% 9 MeV 234 MeV 270 MeV 504 Mev For Fe, B.E./nucleon 9MeV Total B.E  56x9=504 MeV 24

13. B field into screen Radioactive sources detector a particles: nuclei 3 Types of Radioactivity Easily Stopped b- particles: electrons Stopped by metal g : photons (more energetic than x-rays)penetrate! 26

14. 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 momentum. g:example 30

15.  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? 1. Nucleon number decreases by 4 26% 2. Neutron number decreases by 2 45% 3. Charge on nucleus increases by 2 29% Ex. 32

16. 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 34

17. 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 36

18. 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 24% 2 It is cut in half 50% 3 It doubles 26% 38

19. 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 40

20. Decay Function time 40

21. 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: 42

22. 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/s per gram of Carbon. 45

23. Carbon Dating We just determined that living organisms should have a decay rate of about 0.23 events/s per gram of carbon. The bones of an ice man are found to have a decay rate of 0.23/2 events/s per gram. We can estimate he died about 6000 years ago. Example 47

24. At 6,000 years: 50% remains At 12,000 years: 25% remains ACT/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? 1. 3,000 years 2. 6,000 years 3. 12,000 years At 0 years: 100% remains 49

25. 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 50

26. See you next time! • Take a look at Special Relativity in 14 Easy (Hyper)lessons: http://web.hep.uiuc.edu/home/g-gollin/relativity/