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

2. Physics 102: Lecture 27, Slide 2 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)

3. Physics 102: Lecture 27, Slide 3 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! has radius A Z

4. Physics 102: Lecture 27, Slide 4 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

5. Physics 102: Lecture 27, Slide 5 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

6. Physics 102: Lecture 27, Slide 6 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

7. Physics 102: Lecture 27, Slide 7 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|

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

9. Physics 102: Lecture 27, Slide 9 Iron (Fe) is 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

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

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

12. Physics 102: Lecture 27, Slide 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 Preflight 27.4

13. Physics 102: Lecture 27, Slide 13 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

14. Physics 102: Lecture 27, Slide 14  particles: nucleii   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

15. Physics 102: Lecture 27, Slide 15  : 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 energy and momentum.

16. Physics 102: Lecture 27, Slide 16 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

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

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. Preflight 27.7

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

21. Physics 102: Lecture 27, Slide 21 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

22. Physics 102: Lecture 27, Slide 22 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” Preflight 27.8

23. Physics 102: Lecture 27, Slide 23 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” Preflight 27.8

24. Physics 102: Lecture 27, Slide 24 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

25. Physics 102: Lecture 27, Slide 25 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

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

27. Physics 102: Lecture 27, Slide 27 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? 3,000 years 6,000 years 12,000 years

28. Physics 102: Lecture 27, Slide 28 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? 3,000 years 6,000 years 12,000 years At 0 years: 100% remains At 6,000 years: 50% remains At 12,000 years: 25% remains

29. 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”

30. Physics 102: Lecture 27, Slide 30 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/gram of Carbon.

31. Physics 102: Lecture 27, Slide 31 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/gram of Carbon.

32. Physics 102: Lecture 27, Slide 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.

33. Physics 102: Lecture 27, Slide 33 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.

34. Physics 102: Lecture 27, Slide 34 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

35. Physics 102: Lecture 27, Slide 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

36. Physics 102: Lecture 27, Slide 36 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 Survival:

37. Physics 102: Lecture 27, Slide 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