1. Nuclear Binding, Radioactivity Physics 102: Lecture 27 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. 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 neutronproton Very strong force Coulomb force electron proton Strong Nuclear Force (of electron to nucleus)

4. ground state 2.2 MeV Deuterium Binding Energy

5. 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

6. Comparing Nuclear and Atomic sizes Hydrogen Atom: Bohr radius = Nucleus with nucl number A: Note the TREMENDOUS difference Smaller is Bigger! Nucleus is 10 4 times smaller and binding energy is 10 5 times larger! 13 has radius A Z

7. Preflight 27.2 Where does the energy released in the nuclear reactions of the sun come from? (1)covalent bonds between atoms 17% (2)binding energy of electrons to the nucleus 36% (3)binding energy of nucleons 47% 15

8. 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| 17 proton: mc 2 =(1.67x10 -27 kg)(3x10 8 m/s) 2 =1.50x10 -10 J

9. 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 19

10. 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 21

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

12. 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 24 13% 28% 31% 28%

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

14.  : example recall  : example Decay Rules 1)Nucleon Number is conserved. 2)Atomic Number (charge) is conserved. 3)Energy and momentum are conserved.  : example 1)238 = 234 + 4Nucleon number conserved 2)92 = 90 + 2Charge conserved Needed to conserve momentum. 30

15. 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% Preflight 27.6 32  decay is the emission of Ex. Z decreases by 2 (charge decreases!) A decreases by 4

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. 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 36

18. 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% No. of nuclei present decay constant Decays per second, or “activity” Preflight 27.8 38

19. ACT: Radioactivity No. of nuclei present decay constant Decays per second, or “activity” 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 40

20. time 40 Decay Function

21. 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” 42

22. 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. 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. 47

24. 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 49

25. Summary Nuclear Reactions –Nucleon number conserved –Charge conserved –Energy/Momentum conserved –  particles = nucleii –  - particles = electrons –  particles = high-energy photons Decays –Half-Life is time for ½ of atoms to decay 50 Survival:

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/