Important announcements

1. Important announcements • Check gradebook (EX/AB) • Fill out online ICES evaluation • Extra practice problems for final posted online • Next week’s lecture • No Discussion 14 • Lect. 29 next Wed. (May 4) will cover: Disc. 14 problems • FINAL EXAM May 6 & 11 (check online) • Cumulative! ALL MATERIAL COVERED EVENLY • REVIEW Thursday May 5, 1-3pm, 141 Loomis • Extra practice problems (emphasis on Lects. 22-28) • James Scholar projects due next Monday! • Email me word or pdf

2. Physics 102: Lecture 28 Nuclear Binding, Radioactivity

3. Recall: Nuclear Physics A Z Nucleus = Protons + Neutrons nucleons Z = proton number (atomic number) Gives chemical properties (and name) N = neutron number A = nucleon number (atomic mass number) Gives you mass density of element A=N+Z

4. Preflight 27.1 A material is known to be an isotope of lead Based on this information which of the following can you specify? 1) The atomic mass number 2) The neutron number 3) The number of protons Chemical properties (and name) determined by number of protons (Z) Lead Z=82

5. 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 (Isotope of H)

6. Can get 4 nucleons into n=1 state. Energy will favor N=Z # protons = # neutrons Pauli Principle - neutrons and protons have spin like electron, and thus ms= 1/2. But protons repel one another (Coulomb Force) and when Z is large it becomes harder to put more protons into a nucleus without adding even more neutrons to provide more of the Strong Force. For this reason, in heavier nuclei N>Z. 7

7. Deuteron Binding Energy 2.2 MeV ground state

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

9. 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

10. 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|

11. 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

12. 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

13. Preflight 27.3 Which element has the highest binding energy/nucleon? • Neon (Z=10) • Iron (Z=26) • Iodine (Z=53) 37% 19% 44%

14. 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% 39% 31% 17% 9 MeV 234 MeV 270 MeV 504 Mev For Fe, B.E./nucleon 9MeV Total B.E  56x9=504 MeV

15. 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!

16. Example Decay Rules • Nucleon Number (A) is conserved. • Atomic Number (Z) 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

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? 27% 39% 34% 1. Nucleon number decreases by 4 2. Neutron number decreases by 2 3. Charge on nucleus increases by 2 Ex.

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. 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

19. 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

20. No. of nuclei present Decays per second, or “activity” decay constant Radioactive decay rates 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 26% 58% 16%

21. 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

22. Decay Function time

23. 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:

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

25. Survival: Summary • Nuclear Reactions • Nucleon number conserved • Charge conserved • Energy/Momentum conserved • aparticles = nuclei • b-particles = electrons • gparticles = high-energy photons • Decays • Half-Life is time for ½ of atoms to decay