Nuclear physics

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Nuclear Physics Properties of Nuclei Binding Energy Radioactivity Nuclear Components • • • • • • Nucleus contains nucleons: protons and neutrons Atomic number Z = number of protons Neutron number N = number of neutrons Mass number A = number of nucleons = Z + N Each element has unique Z value Isotopes of element have same Z, but different N and A values Notation: A Z X Nucleus Charge and Mass Particle Charge Mass (kg) Mass (u) Mass (MeV/c2) Proton +e 1.672 E−27 1.007 276 938.28 Neutron 1.675 E−27 1.008 665 939.57 Electron −e 9.109 E−31 5.486 E−4 0.511 • Unified mass unit, u, defined using Carbon 12 • Mass of atom of 12C ≡ 12 u u = 1.660 559 ×10 −27 kg = 931.494 MeV c Nuclei Sizes • Scattering experiments determine size • Measured in femtometers (aka fermis) • All nuclei have nearly the same density Fig 29.2, p 959 r = r0 A 13 fm ≡ 10 −15 m [ 29.1] Nuclear Stability • An attractive nuclear force must balance the repulsive electric force • Called the strong nuclear force • Neutrons and protons affected by the strong nuclear force • 260 stable nuclei • If Z > 83, not stable Fig 29.3, p 960 Binding Energy • Total energy of nucleus is less than combined energy of individual nucleons • Difference is called the binding energy (aka mass defect) • Energy required to separate nucleus into its constituents ∆m = ( ∑ mi ) − m A Binding Energy vs Mass Number Fig 29.4, p 961 Radioactivity • Unstable nuclei decay to more stable nuclei • Can emit types of radiation in the process α particles : He nuclei β particles : e − or e + γ rays : high energy photons A positron (e+) is the antiparticle of the electron (e−) Fig 29.5, p 962 Decay Constant and Half-Life • Decay rate (aka activity) is number of decays per second • λ is the decay constant • Unit is Curie (Ci) or Becquerel (Bq) • Decay is exponential • Half-life is time it takes for half of the sample to decay Ci ≡ 3.7 ×1010 decays s Bq = decay s ∆N R= = λN ∆t [ 29.3] N = N e − λt ln 0.693 T1 = = λ λ [ 29.5] [ 29.4a ] Fig 29.6, p 919 Alpha Decay • Unstable nucleus emits α particle (i.e., a helium nucleus) spontaneously • Mass of parent is greater than mass of daughter plus α particle • Most of KE carried away by α particle A Z X→ Fig 29.7, p 966 A− Z −2 Y + He [ 29.8] Beta Decay • Involves conversion of proton to neutron or vice-versa • Involves the weak nuclear force • KE carried away by electron/antineutrino or positron/neutrino pair • Neutrinos: q = 0, m < eV/c2, spin ½, very weak interaction with matter n → p + e +ν A Z X→ p → 01n + e + + ν A Z X → Z −A1Y + e + + ν 1 Fig 29.8a, p 968 1 − A Z +1 Y + e +ν − [ 29.11] [ 29.12] Gamma (γ) Decay • Following radioactive decay, nucleus may be left in an excited state • Undergoes nuclear de-excitation: protons/neutrons move to lower energy level • Nucleus emits high energy photons (γ rays) • No change in A or Z results 12 B → 126C* + e − + ν 12 C* → 126C + γ Radioactive Carbon Dating • Cosmic rays create 14C from 14N • Constant ratio of 14C/ 12C (1.3×10–12) in atmosphere • Living organisms have same ratio • Dead organisms not (no longer absorb C) • T½ of 14C = 5730 yr • Measure decay rates, R R = R0 e − λt ln ( R R0 ) ⇒t =− λ Natural Radioactivity • Three series of naturally occurring radioactivity • 232 238 Thorium Series 235 Th more plentiful than U or U • Nuclear power plants use enriched uranium • Other series artificially produced Fig 29.10, p 971 Nuclear Reactions • Accelerators can • Atomic and mass generate particle numbers (Z and A) must energies up to TeV remain balanced • Bombard a nucleus with • Mass difference before energetic particles and after reaction determines Q value • Nucleus captures the – Exothermic: Q > particle – Endothermic: Q < • Result is fission or fusion • Endothermic requires incoming particle to have KEmin Fusion and Fission Interaction of Radiation with Matter • Radioactive emissions can ionize atoms • Problems occur when these ions (e.g., OH−, H+) react chemically with other ions • Genetic damage affects reproductive cells • Somatic damage affects other cells (lesions, cataracts, cancer, fibrosis, etc.) Quantifying Radioactivity Quantity Definition SI unit Common Unit Activity # nuclei that decay per sec Bq ≡ decay/s Ci = 3.70×1010 Bq Exposure (defined for X and γ rays only) R ≡ amount of radiation that Roentgen (R) Ionization per kg produces 2.58×10−4 C/kg Absorbed Dose (D) Gray (Gy) Energy absorbed per kg ≡ J/kg rad = 10−2 Gy Relative Biological How much more damage is done compared to X or γ Effectiveness (RBE) rays of equivalent energy (unitless) Damage Dose Equivalent (H) expected Sv ≡ RBE×Gy rem = 10−2 Sv RBE Factors Radiation Type X and γ rays RBE Factor 1.0 β particles 1.0−1.7 α particles 10−20 Slow n 4−5 Fast n and p 10 Heavy ions 20 Table 29.3, p 974 Sources of Ionizing Radiation From Touger, Introductory Physics, Table 28-4, p 817 Typical Dose Equivalents From Touger, Introductory Physics, Table 28-4, p 817 Exercise • Is the dose equivalent greater if you are exposed to a 100 mrad dose of α particles or a 300 mrad dose of β particles? α particles: β particles: H = (10 )(100 mrad ) = rem H max = ( 20 )( 300 mrad ) = rem H = (1)(100 mrad ) = 0.1 rem H max = (1.7 )( 300 mrad ) = 0.51 rem α particles are more effective at delivering a dose, but not penetrate as far as β particles [...]... ( R R0 ) ⇒t =− λ Natural Radioactivity • Three series of naturally occurring radioactivity • 232 238 Thorium Series 235 Th more plentiful than U or U • Nuclear power plants use enriched uranium • Other series artificially produced Fig 29.10, p 971 Nuclear Reactions • Accelerators can • Atomic and mass generate particle numbers (Z and A) must energies up to 1 TeV remain balanced • Bombard a nucleus... Factor 1.0 β particles 1.0−1.7 α particles 10−20 Slow n 4−5 Fast n and p 10 Heavy ions 20 Table 29.3, p 974 Sources of Ionizing Radiation From Touger, Introductory Physics, Table 28-4, p 817 Typical Dose Equivalents From Touger, Introductory Physics, Table 28-4, p 817 Exercise • Is the dose equivalent greater if you are exposed to a 100 mrad dose of α particles or a 300 mrad dose of β particles? α particles:...Gamma (γ) Decay • Following radioactive decay, nucleus may be left in an excited state • Undergoes nuclear de-excitation: protons/neutrons move to lower energy level • Nucleus emits high energy photons (γ rays) • No change in A or Z results 12 5 B → 126C* + e − + ν 12 6 C* → 126C + γ Radioactive Carbon
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