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Topic 8 : Nuclear Physics

Topic 8 : Nuclear Physics. Nucleus Nucleons (A) = Protons (Z) + Neutrons (N) Density and stability Radioactivity Formula (exponential decay) Radioactive Processes a , b , and g -rays Natural radioactivity series Fusion/ Fission. Nucleus : Particle Composition.

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Topic 8 : Nuclear Physics

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  1. Topic 8: Nuclear Physics • Nucleus • Nucleons (A) = Protons (Z) + Neutrons (N) • Density and stability • Radioactivity • Formula (exponential decay) • Radioactive Processes • a, b, and g-rays • Natural radioactivity series • Fusion/ Fission Nuclear Physics (Topic 8)

  2. Nucleus: Particle Composition • Z protons + N neutrons = A nucleons (1 – 10 fm dia.). • 1920: Rutherford hypothesized neutron = electron + proton. • Why not? Uncertainty principle violated!(Emin = 100 MeV in 10 Fm) • Nuclear moment too small.(Bohr magneton mB = 2000 × Nuclear magneton mN). • 1932: Chadwick discoveredneutron (new nucleon!). • Isotope: same Z (# protons), different N (# neutrons). • 15O and 16O or 12C and 13C Nuclear Physics (Topic 8)

  3. Nucleus: Particle Properties • Proton, neutron and electron are all fermions (spin 1/2). • Protonandneutron are “heavy” baryons composed of 3 quarks.[proton = up, up, down quarks and neutron = up, down, down]Electron is a “light” lepton. ParticleChargeamuSpinm Proton +e 1.007276 1/2 +2.79mN Neutron 0 1.008665 1/2 – 1.91mN Electron –e 5.4858×10-4 1/2 +1.00mB Nuclear Physics (Topic 8)

  4. Nucleus: Particle Potential Wells • Electron is only bound with negative total energy, and can never escape. • Nucleon can be bound with positive total energy, and can escape by tunneling through the Coulomb barrier  nuclear decay processes. • Leads to radioactive processes. Nucleon Nuclear Potential Electron Coulombic Potential Energy Radius r Nuclear Physics (Topic 8)

  5. Nucleus: Density Distribution • Nucleus has ~uniform density r with radius r. • r = Ro A1/3 where Ro = 1.2 fmr varies by 4× from lightest to heaviest elements. • ratom ~ 103 kg/m3rnucleus = 1017 kg/m3 (mm3 = mass of supertanker!!) He Charge Density r (1025 C/m3) Bi Radial Distance r (fm) Nuclear Physics (Topic 8)

  6. Nucleus: Stability vs. N/Z Ratio Last stable element Z = 83 (Bi) • 3000 known nuclei, but only266 stable ones! • Z > 83 elements not stable! • Tendency for N  Z,but N > Z for larger Z.(due to proton repulsion) • Unusual stability for“magic numbers.” Z, N = 2, 8, 20, 28, 50, 82, 126(analogous to electronic shells) Line of Stability 100 Neutron Number N N = Z 50 50 100 Proton Number Z Nuclear Physics (Topic 8)

  7. Nucleus: Binding Energy B • Nuclear mass is slightly lessthan mass of constituent protons and neutrons due to nuclear binding energy B.Bnuclear = [ Z mHc2 + N mnc2 ] – [ MAc2 ] where mH = 1.007825amu and mn = 1.008665 amu  Parts Whole • Binding energy per nucleon peaks at A = 56(~8 MeV/nucleon) and slowly decreases. • Energy is released when a heavy nucleus (A~200) fissions into lighter nuclei near A~60. Peaks at Fe (A = 56) Fission (A ~ 200) Binding Energy / Nucleon ( MeV) Nucleon Number A Nuclear Physics (Topic 8)

  8. Radioactivity: Historical Overview • 1896: Becquerelaccidentally discovered that uranyl crystals emitted invisible radiation onto a photographic plate. • 1898: Marie and Pierre Curie discovered polonium (Z=84) and radium (Z = 88), two new radioactive elements. • 1903: Becquerel and the Curie’s received the Nobel prize in physics for radioactive studies. • 1911: Marie Curie received a 2ndNobel prize (in chemistry) for discovery of polonium and radium. • 1938: Hahn (1944 Nobel prize) and Strassmann discovered nuclear fission - Lisa Meitner played a key role! • 1938: Enrico Fermi received the Nobel prize in physics for producing new radioactive elements via neutron irradiation, and work with nuclear reactions. Nuclear Physics (Topic 8)

  9. Radioactivity: Why? Neutron Dripline • Number of protons & neutronsin nucleus islimited. • Limits marked by driplines(outside dripline, nucleus spontaneously emits proton or neutron). • Nuclei decay to stable isotopes (Z  83) via radiation. • Initial mass of a radioactive nucleus is greater than its final mass plus any decay product masses. (E = mc2) Line of Stability 100 Neutron Number N 50 Proton Dripline 50 100 Proton Number Z Nuclear Physics (Topic 8)

  10. Radioactivity: Relevant Equations • Radioactivity is the decay of nuclei to more stable configurations via emission of “radiation” (a or b particles,  rays, etc.). • Decay rate dN/dt is proportional to the number of nuclei N, leading to a 1st order differential equation with an exponential solution. • where l = decay constantt = 1/l = lifetime (or 37% original), t1/2 = half-life (50% original) Nuclear Physics (Topic 8)

  11. Radioactivity: Graphical Representation • Quick formula: • (rate %) (half-life in yrs) = 70 • Where is the 70 from? • If an animal species is dying at a 10% annual rate, how long until the population is halved? • If you have a 5% return on your money, how long until it is doubled? • If you double your money in 7 years, what is the growth rate? Nuclear Physics (Topic 8)

  12. Radioactivity: Overview of Units • Activity: Becquerel (Bq) = 1 decay / s 1 curie (Ci) = 3.7×1010 decays / s (or Bq) (disintegration rate of 1g of radium) • Ion Dose: Ionizing behavior of radiation is most damaging to us!Roentgen= 2.6×10–4 C/ kgair (or 0.0084 j/kg) • Energy Dose: rad= 0.01 j/kg • Energy Dose for Human Health Considerations:rem = # rads × quality factor (a = 10 and b,g = 1) • Dosages: 0.5 rem / yr = natural background 5 rem / yr = limit for nuclear power plant workers 500 rem = 50% die within a month750 rem = fatal dose (5000 rem = die within 1 week) Nuclear Physics (Topic 8)

  13. Radioactivity:Half-life/Rate Problem • The counting rate R from a radioactive source is 1000 s–1 at timet = 0, and 250 s–1 at time t = 5 s. Find the half-life t1/2 and the rate R at t = 12 s. Nuclear Physics (Topic 8)

  14. Radiation Processes:a, b, g × × × × × × × × × × × × × × × × × × × × a g e– B field Type of RadiationCharge/MassPenetration alpha a= He nucleus (2p + 2n) +2q/4mp sheet of paper beta b = electron or positron –q/me or +q/me few mm metal gamma g = high-energy photon no charge several cm lead Nuclear Physics (Topic 8)

  15. Radiation Processes: Alpha Decay a Before After • Parent nucleus decays to daughter nucleus plus an alpha particle. • Disintegration energy Q appears as kinetic energy.(= negative binding energy) • Lighter a particle carries away most of the kinetic energy. • Why? Conservation of momentum! Parent Daughter where mHe = 4.002603amu Nuclear Physics (Topic 8)

  16. Radiation Processes: b– Decay (e– Emission) • Parent nucleus decays to daughter nucleus plus electron and anti-neutrino. • Anti-neutrino is 3rd particle that explains range of electron kinetic energies. • If atom (Z) has greater mass than its right neighbor (Z+1), then b– decay is possible. • Free neutroncan decay into a proton. • t1/2 = 10.8 min, Q = 939.57 – (938.28 + 0.511) = 0.78 MeV Nuclear Physics (Topic 8)

  17. Radiation : b– Decay for Carbon Dating • b-decay of 14C used to date organic samples. • 14C  14N + e– + ne • When organisms are alive, cosmic rays create14C in atmosphere to give constant 14C/12C ratio in CO2 gas. • 14C / 12C = 1.2×10–12 in living organism • When organisms die, 14C is no longer absorbed and 14C/12C ratio decreases with time. • Half-life t1/2 of 14C = 5730 yr. • Measure age of material by finding 14C activity per unit mass. • Effective for 1,000 to 25,000 years ago. Nuclear Physics (Topic 8)

  18. Radiation Processes: b+ Decay (Positron Emission) • Parent nucleus decays to daughter nucleus plus positron and neutrino. • Free protoncannot decay into a neutron via positron emission. • Contrasts free neutron decay into a proton. • Bound proton inside nucleus can sometimes emit a positron due to nuclear binding energy effects. • Only natural positron emitter is 40K. Nuclear Physics (Topic 8)

  19. Radiation Processes: Electron Capture • Parent nucleus captures one of its own orbital electrons and converts a nuclear proton to a neutron. • If atom (Z) has greater mass than its left neighbor (Z–1), then electron capture is possible. • Note: If mass difference between atom (Z) and neighboring atom (Z–1) is greater than 2me, then positron decay is also possible. Nuclear Physics (Topic 8)

  20. Radiation Processes: Gamma Decay • In gamma decay, an excited-state nucleus decays to a lower energystate via photonemission. • Such nuclear transitions areanalogous to atomic transitions, but with higherenergy photons.l = 1240 eV nm / Mev = 10–3 nm. • g-ray emission usually follows beta decay or alpha decay (see figure). • Mean lifetimes are very short.t = hbar / DE = 10–10 s Nuclear Physics (Topic 8)

  21. Radiation Processes:Decay Energy Problem • 80Br can undergo all three types of  decay. In each case,(a) write down the decay equation and (b) find the decay energy Q. • – Decay Process:80Br 80Kr + e– + e • Q(–) = M( 80Br)c2 – M( 80Kr)c2 • = 79.918528 uc2 – 79.916377 uc2 • Q(–) = (0.002151 uc2) (931.5 MeV/uc2) = 2.00 MeV • + Decay Process:80Br 80Se + e+ + e • Q(+) = M( 80Br)c2 – M( 80Se)c2 – 2mec2 • = 79.918528 uc2 – 79.916519 uc2 – 2(5.4858×10–4)uc2 • Q(+) = (0.00091184 uc2) (931.5 MeV/uc2) = 0.85 MeV • e– captureDecay Process:80Br + e–80Se + e • Q(ec) = M( 80Br)c2 – M( 80Se)c2 • = 79.918528 uc2 – 79.916519 uc2 • Q(ec) = (0.002009 uc2) (931.5 MeV/uc2) = 1.87 MeV Nuclear Physics (Topic 8)

  22. Radiation Processes: Natural Radioactivity • Three series of naturally occurring radioactive nuclei. • Start with radioactive isotope (U, Th) and end with isotope of Pb. • Fourth series starts with an element not found in nature (237Np). • A few other naturally occurring radioactive isotopes occur (14C, 40K). Nuclear Physics (Topic 8)

  23. Fusion and Fission: Why? • Plot Mass DifferenceDM (= M– Zmp – Nmn) vs. Nucleon Number A. • Equals “Inverse” of graph for Binding Energy vs. A. • Elements with highDM have unstable nuclei. • Decay via fusion (low A) or fission (high A) to form more stable nuclei. • Total mass decreases and energy is released! Why?? E = mc2 Fission (A ~ 200) Fusion DMass / nucleon (MeV/c2) Nucleon Number A Nuclear Physics (Topic 8)

  24. Fission: Process • Neutron collideswith a 235U nucleus to form an excited state that decays into two smaller nuclei (plus neutrons) plus ENERGY! • Example: 235U + n 92Kr + 142Ba + 2n + 180 MeV • (238U does not work!) 235U will not fission without being “kicked” by neutron. Nuclear Physics (Topic 8)

  25. Fission: Chain Reaction • Use neutrons from fission process to initiate other fissions! • 1942: Fermi achieved first self-sustaining chain reaction. • For nuclear bomb, need more than one neutron from first fission event causing a second event. • For nuclear power plant, need less than one neutron causing a second event. Nuclear Physics (Topic 8)

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