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)
Radioac ve Decay
• Antoine Henri Becquerel • Marie Curie, née Sklodowska • Pierre Curie
Nobel Prize in 1903
2 Laws of Radioac ve Decay
• Ac vity: 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 Radioac ve Decay
• Radia on from a radioac ve sample is due to decay of many independent nuclei. • Let each nuclei have a probability of decay per unit me given by λ. • The ac vity at me t is given by the probability mes the number of nuclei at me t. R = λN(t)
3 Laws of Radioac ve 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 Radioac ve Decay
• Half life: me 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 Ra os
5 Half-lives
Decay Energe cs
• All Decays: – Energy, Momentum, Angular Momentum • Strong Interac on and Electromagne c decays: – N and Z conserved, Parity Conserved • Weak Interac on decays: – Atomic number, A, conserved • A Nuclide is unstable if – There is another nucleon configura on with a lower total energy. – There is a process that can reach the configura on while obeying the conserva on 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 ra os • For A < 40: N ≈ Z • For A > 40: N > Z
Q-value: Disintegra on 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 par cles are helium nuclei.
A A−4 Z X →Z −2Y +α
• Alphas formed inside the nucleus tunnel out of the coulomb barrier.
10 Alpha Decay and Smoke Detectors
• Smoke detectors are ioniza on chambers. • The alpha’s emi ed by the Americium-241 ionize the air between the plates allowing a current to flow between the plates. • When smoke enters the detector the par cles 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 par cles are electrons. • One of a class of weak interac on decays.
12 Beta Decay
• Weak interac on 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
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 characteris c x- ray and electron spectra associated with IC dis nguish it from beta decay.
17 Gamma Decay
• Gamma decay o en 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 Radioac ve Series • Four decay series contain most of the common radionuclides • Each series consists of a succession of daughter products ul mately derived from a single parent.
Radioac ve 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 • Ac nium (A = 4n+3) 235 207 92U 82 Pb
21 Radioac ve Da ng
• 204Pb – stable and not a daughter of any nuclide • 206Pb and 207Pb are the end of decay chains. • Ra o of 207Pb/ 204Pb is roughly constant as the half- life of the Ac nium chain is short ~7 x 108 yrs. • Ra o of 206Pb/ 204Pb is s ll changing as the Uranium 9 chain has thalf ~ 4.5 x 10 yrs. • Comparison of the two ra os 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