Nothing in life is to be feared. It is only to be understood. -Marie Curie Segre Chart (Table of Nuclides) Z N 1 Segre Chart (Table of Nuclides) Radioac8ve Decay • Antoine Henri Becquerel • Marie Curie, née Sklodowska • Pierre Curie Nobel Prize in 1903 2 Laws of Radioac8ve Decay • Ac8vity: dN R = − dt • N = number of nuclei • Units: – 1 Becquerel (Bq) = 1 decay/s – 1 Curie (Ci) = 3.7 x 1010 decays/s Laws of Radioac8ve Decay • Radiaon from a radioac8ve sample is due to decay of many independent nuclei. • Let each nuclei have a probability of decay per unit 8me given by λ. • The ac8vity at 8me t is given by the probability 8mes the number of nuclei at 8me t. R = λN(t) 3 Laws of Radioac8ve Decay • The number of nuclei that decay in dt is given by dN(t) = −Rdt = −λN(t)dt −λt N(t) = N0e −λt R = R0e Laws of Radioac8ve Decay • Half life: 8me in which the number of nuclei drops to half its original value. ln 2 0.693 t1/ 2 = = λ λ 4 Daughter Products • As one nuclide decays it creates another. Branching Raos 5 Half-lives Decay Energecs • All Decays: – Energy, Momentum, Angular Momentum • Strong Interac8on and Electromagne8c decays: – N and Z conserved, Parity Conserved • Weak Interac8on decays: – Atomic number, A, conserved • A Nuclide is unstable if – There is another nucleon configuraon with a lower total energy. – There is a process that can reach the configuraon while obeying the conservaon rules. 6 General Criteria for Stability • All isotopes with Z > 83 are unstable. • Pairing: • Most even-even nuclei are stable • Many odd-even or even-odd nuclei are stable. • Only 4 odd-odd nuclei are stable. (2H, 6Li, 10B, 14N) • N/Z raos • For A < 40: N ≈ Z • For A > 40: N > Z Q-value: Disintegraon Energy • The q-value is the energy difference between the parent nuclide and the daughter products. A 2 Q = [M (Z X )− M (products)]c • If Q > 0 then the nucleus is unstable and will decay into the daughter products. 7 Decay Processes Comparing “Rays” α β γ Cardboard Aluminum Lead 8 Types of Decay Alpha Decay • Alpha par8cles are helium nuclei. A A−4 Z X →Z −2Y +α 9 Alpha Decay • Alphas formed inside the nucleus tunnel out of the coulomb barrier. 10 Alpha Decay and Smoke Detectors • Smoke detectors are ionizaon chambers. • The alpha’s emiied by the Americium-241 ionize the air between the plates allowing a current to flow between the plates. • When smoke enters the detector the par8cles combine with the ions and neutralize the air. The current reduces causing the detector alarm to sound. 11 Beta-minus Decay Beta-minus Decay • Beta-minus par8cles are electrons. • One of a class of weak interac8on decays. 12 Beta Decay • Weak interac8on can transform protons ⇔ neutrons • Beta-minus: n → p + e− +ν • Beta-plus: p → n + e+ +ν • Electron capture: p + e− → n +ν Beta decay • Beta-minus: A A − Z X →Z +1Y + e +ν • Beta-plus: A A + Z X →Z −1Y + e +ν • Electron capture: A − A Z X + e →Z −1Y +ν 13 Valley of Stability Z N Odd A Isobar Plot 14 Even A Isobar Plot The Neutrino Hypothesis 15 Neutrino Mass Neutrino Mass 16 Gamma-Decay • Rearrangement of nucleons in nucleus with the emission of a photon. A * A Z X →Z X + γ • Gamma-ray energies are ~ 1 MeV and higher. Internal Conversion • Rather than emit a gamma-ray the nucleus can transfer energy to one of the atomic electrons. • The characteris8c x- ray and electron spectra associated with IC dis8nguish it from beta decay. 17 Gamma Decay • Gamma decay omen follows either alpha or beta decay. • The parent nucleus decays to an excited state in the daughter which de-excites via gamma emission or internal conversion. Quiz 1 18 Quiz 2 Nucleon Emission 19 Decay Processes on the Segre Chart Spontaneous Fission 20 Radioac8ve Series • Four decay series contain most of the common radionuclides • Each series consists of a succession of daughter products ul8mately derived from a single parent. Radioac8ve Series (Decay Chains) • Thorium (A = 4n) 232 208 90Th 82 Pb • Neptunium (A = 4n+1) 237 209 93 Np 83 Bi • Uranium (A = 4n+2) 238 206 92U 82 Pb • Ac8nium (A = 4n+3) 235 207 92U 82 Pb 21 Radioac8ve Dang • 204Pb – stable and not a daughter of any nuclide • 206Pb and 207Pb are the end of decay chains. • Rao of 207Pb/ 204Pb is roughly constant as the half- life of the Ac8nium chain is short ~7 x 108 yrs. • Rao of 206Pb/ 204Pb is s8ll changing as the Uranium 9 chain has thalf ~ 4.5 x 10 yrs. • Comparison of the two raos can give the age of a sample. 22 Shroud of Turin Very small samples from the Shroud of Turin have been dated by accelerator mass spectrometry in three independent laboratories. As Controls, three samples whose ages had been determined independently were also dated. • The results of radiocarbon measurements at Arizona, Oxford and Zurich yield a calibrated calendar age range with at least 95% confidence for the linen of the Shroud of Turin of AD 1260 - 1390 (rounded down/up to nearest 10 yr). These results therefore provide conclusive evidence that the linen of the Shroud of Turin is mediaeval. – (Nature, Vol. 337, No. 6208, pp. 611-615, 16th February, 1989 ) 23 .