# Nuclear Physics. Remember: Particles have a wave nature. Only certain wavelengths meet the boundary conditions, so only certain energies are allowed.

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1 Nuclear Physics The forces holding together the nucleus are large. And so are the energies involved. Radioactivity is a natural process. Certain nuclei fall apart and emit ionizing radiation as they do. Radiation and radioactivity are dangerous but useful. They can cause illness, but they can cure or diagnose as well. 1 Where Are We Headed? Lecture: Monday, April 8:!! Nuclear Physics Basics Wednesday, April 10: Nuclear Physics Applications Friday, April 1:!! Duck and Cover: Tales of the Atomic Age Monday, April 15:!! Applications to Bodies and the Biosphere Wednesday, April 17:! Exam # Review Friday, April 19:!! Exam # Exam: Exam # is on Friday, April 19. Practice Exam posted Monday, April 15. Remember: Particles have a wave nature. Only certain wavelengths meet the boundary conditions, so only certain energies are allowed. 3

2 The Nucleus Confining neutrons and protons in the box of the nucleus means that their allowed energies are enormous. Changing Scale The diameter of a typical atomic nucleus is about 10 fm. (1 fm is 1x10-15 m.) What are the particle in a box energy states for a proton in a 1D box of this size? E n = 1 m hn L = h 8mL n n = 1,,3,... 5 The Nucleus Number of protons determines the element, number of neutrons the isotope. 6

3 Most elements have more than one stable isotope. We will never use this number. Never. Notation Mass of an atom: e.g. chlorine Mass number: A=Z+N ) Never acceptable: Using atomic weights from the periodic table. U ) Quick and dirty: Use mass number: 35Cl: mass = 35 u Atomic number: Z 3) For energy calcs: Use data from Appendix D: 35Cl: mass = u Z = # of protons N = # of neutrons 8 Notation How many neutrons are in each of the following nuclei? 11 3 Li 11 Be 11 5 B 11 6 C A. 8 B. 7 C. 6 D. 5 9

4 More 18 8 O Warmer Less 18 8 O Cooler Oxygen 18 variation from average (%) Isotopes Years before present 10 Boron, atomic number Z=5, has two stable isotopes, with atomic mass numbers A=10 and A=11. Boron s chemical atomic mass is What are the approximate fractions of the two stable boron isotopes found in nature?! A.!! 9% 11B,! 8% 10B! B.!! 80% 11B,! 0% 10B! C.!! % 11B,! % 10B! D.!! 0% 11B,! 80% 10B! E.!! 8% 11B,!! 9% 10B 11 Holding it All Together Helium nucleus neutron proton An especially stable combo Strong force n n n p p p Coulomb force 1

5 Stability Neutron number N Stable isotope Unstable isotope Too many neutrons Too big; Coulomb repulsion too strong Bismuth, Z 5 83 Just right. N 5 Z line He 1 C 16 O Line of stability 10 Too few neutrons Proton number Z 13 Energy Levels in the Nucleus Energy (MeV) Neutrons 0 n 5 3 n 5 Protons n 5 3 n 5 n 5 1 n 5 1 For light nuclei, neutron and proton energy levels are about the same. 1 Beta Decay Energy U (MeV) (Mev) 0 11 Be Neutrons Protons 15

6 Beta Decay 11 5 U (MeV) Energy (Mev) B 0 Neutrons Protons 11 Be 115 B + 10 e16 Alpha Decay Parent nucleus Nucleus too darn big. And it does. Wants to break apart. Before: A XZ After: A YZ Daughter nucleus 38 9 U 3 90 Alpha particle Th + α 17 When atoms decay, they don t disappear U 3 90 Th + α 18

7 Gamma Decay Excited level Lower level Gamma-ray photon 99 Mo Excited state Beta decay e 99 Tc * Gamma decay g Ground state 99 Tc 19 Determining the Daughter Nucleus! 90 Sr? X + e - A. 90 Y B. 89 Y C. 90 Rb D. 89 Rb! Rn? X + α A. 0 Po B. 18 Po C. 0 Ra D. 18 Ra 0 Determining the Decay Mode What is the decay mode of the following decays? 137 Cs 137 Ba +?! A.!! alpha decay! B.!! beta-minus decay! C.!! beta-plus decay! D.!! gamma decay Rn 18 Po +?! A.!alpha decay! B.!beta-minus decay! C.!beta-plus decay! D.!gamma decay 1

8 11Be is an unstable isotope of beryllium. Sketch the energy level structure for the neutrons and the protons in this nucleus. What decay mode would you expect for this nucleus? Energy (MeV) 0 Neutrons n53 n5 n51 Protons n53 n5 n51 Properties of Radiation alpha least penetrating gamma most penetrating 3 Nuclear Radiation is Ionizing Radiation Operation of Geiger counter Radiation burn from cancer treatment

9 Radiation is Part of Your Life 5 You Light Up My Half Life t t 1 1/ N = N 0 6 Chernobyl Cheese The Chernobyl nuclear reactor accident in the Soviet Union in 1986 released a large plume of radioactive isotopes into the atmosphere. Of particular health concern was the short-lived (half life: 8.0 days) isotope 131 I, which, when ingested, is concentrated in and damages the thyroid gland. This isotope was deposited on plants that were eaten by cows, which then gave milk with dangerous levels of 131 I. This milk couldn t be used for drinking, but it could be used to make cheese, which can be stored until radiation levels have decreased. How long would a sample of cheese need to be stored until the number of radioactive atoms decreased to 3% of the initial value? t t 1 1/ N = N 0 7

10 Decay is a Random Process 1 N = N0 t t1/ 8 Short half life means high activity. activity = decay rate = R = 38Pu, half 0.693N t1/ life 88 years 9 Half Life and Activity There are two main isotopes of uranium, 35U and 38U. Two billion years ago, 35U comprised 3% of the uranium in the earth s crust. Now, it s prevalence has dropped to 0.7% of the uranium in the earth s crust. Which of the isotopes has a longer half life? If you have a sample of 35U and a sample of 38U, each with the same mass (and therefore approximately the same mass) which sample will have a higher activity? 1 N = N0 t t1/ R= 0.693N t1/ 30

11 A small sample can give a big count rate. 31 Relationships Decay: 1 N = N0 t t1/ Activity: t1/ tt 1 1 R = R0 R = rn = 3 t tt t 11 1/1/ N R == RN0 0 My watch has a tritium (t1/ = 1 yr) dial. When I purchased it in 00, it had an activity of about 100 MBq. What is the activity now? 33

12 Radioactive Dating A scrap of parchment from the Dead Sea Scrolls was found to have a 1C/1C ratio that is 79.5% of the modern value. 1 N = N0 Determine the age of this parchment. t t1/ Relevant data from Appendix D: t1/ = 5730 yr 3 Special Relativity Mass-energy conversion The most famous equation in the world: E = mc 1u is equivalent to MeV 35 Antimatter A positron is an anti-electron: Same mass, but positive charge 36

13 What, in MeV, is the minimum energy gamma ray that can give rise to an electron-positron pair? 37 Binding Energy Helium: Binding energy per nucleon: MeV crucial conversion 38 Binding Energy What is the binding energy per nucleon of 56Fe?! Mass of 56Fe:!! ! Mass of 1H:!! ! Mass of n:!!! u is equivalent to MeV 39

14 Can get energy by fusion Can get energy by fission 0 Fission A nucleus of 0Pu can be induced to fission into smaller fragments. What are the binding energies per nucleon of 0Pu and the possible fission product 133Xe? Data from Appendix C: Nucleus!! Atomic mass 0Pu:!!! Xe:!!! H:!!!! n:!!!! u is equivalent to MeV 1 Fusion Rounding slightly, the nucleus 3He has a binding energy of.5 MeV per nucleon; 6Li has a binding energy of 5.0 MeV per nucleon. Would it be energetically possible for two 3He nuclei to fuse together to form a nucleus of 6Li? If so, how much energy would be released in the reaction? (Ignore the exact details of how the reaction would go.)

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