Published on October 15, 2007
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: 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 discovered neutron (new nucleon!). Isotope: same Z (# protons), different N (# neutrons). 15O and 16O or 12C and 13C Nucleus: Particle Properties: Nucleus: Particle Properties Proton, neutron and electron are all fermions (spin 1/2). Proton and neutron are “heavy” baryons composed of 3 quarks. [proton = up, up, down quarks and neutron = up, down, down] Electron is a “light” lepton. Particle Charge amu Spin m 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 Nucleus: Particle Potential Wells: 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. Electron Coulombic Potential Nucleon Nuclear Potential Energy Radius r Nucleus: Density Distribution: Nucleus: Density Distribution Nucleus has ~uniform density r with radius r. r = Ro A1/3 where Ro = 1.2 fm r varies by 4× from lightest to heaviest elements. ratom ~ 103 kg/m3 rnucleus = 1017 kg/m3 (mm3 = mass of supertanker!!) Radial Distance r (fm) Charge Density r (1025 C/m3) He Bi Nucleus: Stability vs. N/Z Ratio: Nucleus: Stability vs. N/Z Ratio 3000 known nuclei, but only 266 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 N = Z Proton Number Z Neutron Number N 100 50 100 50 Last stable element Z = 83 (Bi) Nucleus: Binding Energy B: Nuclear mass is slightly less than 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 Nucleus: Binding Energy B 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. Parts Whole Nucleon Number A Binding Energy / Nucleon ( MeV) Peaks at Fe (A = 56) Fission (A ~ 200) Radioactivity: Historical Overview: Radioactivity: Historical Overview 1896: Becquerel accidentally 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 2nd Nobel 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. Radioactivity: Why?: Radioactivity: Why? Number of protons & neutrons in nucleus is limited. 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 Proton Number Z Neutron Number N 100 50 100 50 Neutron Dripline Proton Dripline Radioactivity: Relevant Equations: 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 constant t = 1/l = lifetime (or 37% original), t1/2 = half-life (50% original) Radioactivity: Graphical Representation: 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? Radioactivity: Overview of Units: 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 month 750 rem = fatal dose (5000 rem = die within 1 week) Radioactivity: Half-life/Rate Problem: Radioactivity: Half-life/Rate Problem The counting rate R from a radioactive source is 1000 s–1 at time t = 0, and 250 s–1 at time t = 5 s. Find the half-life t1/2 and the rate R at t = 12 s. Radiation Processes: a, b, g: Radiation Processes: a, b, g Type of Radiation Charge/Mass Penetration 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 Radiation Processes: Alpha Decay: Radiation Processes: Alpha Decay 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! Before a After Parent Daughter where mHe = 4.002603amu Radiation Processes: b– Decay (e– Emission): 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 neutron can decay into a proton. t1/2 = 10.8 min, Q = 939.57 – (938.28 + 0.511) = 0.78 MeV Radiation : b– Decay for Carbon Dating: 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 create 14C 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. Radiation Processes: b+ Decay (Positron Emission): Radiation Processes: b+ Decay (Positron Emission) Parent nucleus decays to daughter nucleus plus positron and neutrino. Free proton cannot 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. Radiation Processes: Electron Capture: 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. Radiation Processes: Gamma Decay: Radiation Processes: Gamma Decay In gamma decay, an excited-state nucleus decays to a lower energy state via photon emission. Such nuclear transitions are analogous to atomic transitions, but with higher energy 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 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– capture Decay 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 Radiation Processes: Decay Energy Problem Radiation Processes: Natural Radioactivity: 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). Fusion and Fission: Why?: Fusion and Fission: Why? Plot Mass Difference DM (= M– Zmp – Nmn) vs. Nucleon Number A. Equals “Inverse” of graph for Binding Energy vs. A. Elements with high DM 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 Nucleon Number A DMass / nucleon (MeV/c2) Fission (A ~ 200) Fusion Fission: Process: Fission: Process Neutron collides with 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. Fission: Chain Reaction: 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.