1. Physics 102: Lecture 27, Slide 1 Important announcements Check gradebook (EX/AB) Fill out online ICES evaluation Extra practice problems for final posted onlineExtra practice problems 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 27, Slide 2 Nuclear Binding, Radioactivity Physics 102: Lecture 28

3. Physics 102: Lecture 27, Slide 3 Nucleus = Protons + Neutrons nucleons A = nucleon number (atomic mass number) Gives you mass density of element Z = proton number (atomic number) Gives chemical properties (and name) N = neutron number A=N+Z Recall: Nuclear Physics A Z

4. Physics 102: Lecture 27, Slide 4 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 LeadZ=82 Preflight 27.1 Chemical properties (and name) determined by number of protons (Z)

5. Physics 102: Lecture 27, Slide 5 Hydrogen atom: Binding energy =13.6eV Binding energy of deuteron = or 2.2Mev! That’s around 200,000 times bigger! Simplest Nucleus: Deuteron=neutron+proton (Isotope of H) neutronproton Very strong force Coulomb force electron proton Strong Nuclear Force (of electron to nucleus)

6. Physics 102: Lecture 27, Slide 6 Can get 4 nucleons into n=1 state. Energy will favor N=Z Pauli Principle - neutrons and protons have spin like electron, and thus m s =  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. # protons = # neutrons 7

7. Physics 102: Lecture 27, Slide 7 ground state 2.2 MeV Deuteron Binding Energy

8. Physics 102: Lecture 27, Slide 8 Nuclei have energy level (just like atoms) 12 C energy levels Note the energy scale is MeV rather than eV energy needed to remove a proton from 12 C is 16.0 MeV energy needed to remove a neutron from 12 C is 18.7 MeV

9. Physics 102: Lecture 27, Slide 9 Preflight 27.2 Where does the energy released in the nuclear reactions of the sun come from? (1)covalent bonds between atoms (2)binding energy of electrons to the nucleus (3)binding energy of nucleons

10. Physics 102: Lecture 27, Slide 10 Binding Energy Einstein’s famous equation E = m c 2 Proton: mc 2 = 938.3MeV Neutron: mc 2 = 939.5MeV Deuteron: mc 2 =1875.6MeV Adding these, get 1877.8MeV Difference is Binding energy, 2.2MeV M Deuteron = M Proton + M Neutron – |Binding Energy| proton: mc 2 =(1.67x10 -27 kg)(3x10 8 m/s) 2 =1.50x10 -10 J

11. Physics 102: Lecture 27, Slide 11 ACT: Binding Energy Which system “weighs” more? 1)Two balls attached by a relaxed spring. 2)Two balls attached by a stretched spring. 3)They have the same weight. M 1 = M balls + M spring M 2 = M balls + M spring + E spring /c 2 M 2 – M 1 = E spring /c 2 ~ 10 -16 Kg

12. Physics 102: Lecture 27, Slide 12 Iron (Fe) has most binding energy/nucleon. Lighter have too few nucleons, heavier have too many. BINDING ENERGY in MeV/nucleon 10 Binding Energy Plot Fission Fusion Fusion = Combining small atoms into large Fission = Breaking large atoms into small

13. Physics 102: Lecture 27, Slide 13 Which element has the highest binding energy/nucleon? Preflight 27.3 Neon (Z=10) Iron (Z=26) Iodine (Z=53) 37% 19% 44%

14. Physics 102: Lecture 27, Slide 14 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 has 56 nucleons Total B.E  56x9=504 MeV Preflight 27.4 13% 39% 31% 17%

15. Physics 102: Lecture 27, Slide 15  particles: nuclei   particles: electrons  : photons (more energetic than x-rays) penetrate! 3 Types of Radioactivity Easily Stopped Stopped by metal Radioactive sources B field into screen detector

16. Physics 102: Lecture 27, Slide 16  : example recall  : example Decay Rules 1)Nucleon Number (A) is conserved. 2)Atomic Number (Z) is conserved. 3)Energy and momentum are conserved.  : example 1)238 = 234 + 4Nucleon number conserved 2)92 = 90 + 2Charge conserved Needed to conserve momentum.

17. Physics 102: Lecture 27, Slide 17 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 Preflight 27.6  decay is the emission of Ex. Z decreases by 2 (charge decreases!) A decreases by 4 27% 39% 34%

18. Physics 102: Lecture 27, Slide 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. Physics 102: Lecture 27, Slide 19 ACT: Decay Which of the following decays is NOT allowed? 1 2 3 4 238 = 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

20. Physics 102: Lecture 27, Slide 20 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 No. of nuclei present decay constant Decays per second, or “activity” Radioactive decay rates Preflight 27.8 26% 58% 16%

21. Physics 102: Lecture 27, Slide 21 ACT: Radioactivity Start with 16 14 C atoms. After 6000 years, there are only 8 left. How many will be left after another 6000 years? 1) 02) 43) 8 Every 6000 years ½ of atoms decay No. of nuclei present decay constant Decays per second, or “activity”

22. Physics 102: Lecture 27, Slide 22 time Decay Function

23. Physics 102: Lecture 27, Slide 23 Instead of base e we can use base 2: Survival: No. of nuclei present at time t No. we started with at t=0 where Then we can write Half life Radioactivity Quantitatively No. of nuclei present decay constant Decays per second, or “activity”

24. Physics 102: Lecture 27, Slide 24 You are radioactive! One in 8.3x10 11 carbon atoms is 14 C which   decays with a ½ life of 5730 years. Determine # of decays/s per gram of Carbon.

25. Physics 102: Lecture 27, Slide 25 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.

26. Physics 102: Lecture 27, Slide 26 ACT/Preflight 27.9 The half-life for beta-decay of 14 C is ~6,000 years. You test a fossil and find that only 25% of its 14 C 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 At 6,000 years: 50% remains At 12,000 years: 25% remains

27. Physics 102: Lecture 27, Slide 27 Summary Nuclear Reactions –Nucleon number conserved –Charge conserved –Energy/Momentum conserved –  particles = nuclei –  - particles = electrons –  particles = high-energy photons Decays –Half-Life is time for ½ of atoms to decay Survival: