Spring 2018 PTYS 510A

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1 Spring 2018 PTYS 510A Building Blocks of Matter Nuclear Systematics Chart of the Nuclides Radioactive Decay

2 Atomic Structure Protons (Z), neutrons (N), collectively referred to as nucleons, and electrons Neutral atom Atomic # (Z) = # of protons = number of electrons Atomic mass (A) = Z + N Isotopes of an element have same Z, different N, and hence, different A

3 Isotopes How do we change A? Each element consists of 1 to 10 stable isotopes Unstable = radioactive decay, i.e., radiogenic Oxygen (Z = 8): 8 protons, 8, 9, or 10 neutrons giving: 16 O (99.63%), 17 O (0.0375%), 18 O (0.1995%) Hydrogen: (Z=1): 1 proton, 0 or 1 neutron giving: 1 H ( %) and 2 H %

4 Isotope Notation Mass # 16 O 2 0 Charge state stoichiometry Read as oxygen sixteen, NOT, 16-O (although you ll hear this said at meetings ) Mass (A) or Nucleon # Z 14 C 6 14 C

5 Atomic Mass Masses of atoms described in atomic mass units, u (also called Dalton or Da) Defined as 1/12 12 C 1.66x10-27 kg 6 In other words, mass of 12 C is arbitrarily fixed at amu 6 All other nuclides and subatomic particles are measured relative to amu More convenient to use gram atomic weight or mole #atoms or molecules/mole =? When discussing isotopes of more than one element, we use nuclide

6 Atomic Weight Atomic weight of an element is the sum of the masses of its naturally occurring isotopes, weighted in accordance with the abundance of each isotope Isotope Mass Abundance Weighted Mass 35 Cl Cl Atomic Weight amu

8 Nuclide Mass Can we calculate mass of nuclide by adding mass of protons + electrons (M P = amu) and neutrons (M N = amu)? Observed masses < calculated masses Mass defect? Why? PE of stable nucleus < constituent particles PE converted to thermal energy when nucleus forms Cooled system has lower mass than sum of particles Mass of nuclear particles converted to binding energy = nuclear glue E B = ΔMc 2, where E B = binding energy, ΔM = mass defect, c = velocity of light = x10 10 cm/s

9 Binding Energy How much energy in 1 amu? Calculation

10 Binding Energy Binding energies per nucleon of the atoms of most elements range from 7.5 to 8.8 MeV H, He, Li, and Be have lower E B Other elements, E B / nucleon rises slight w/increase in A Reaches a maximum at 56 Fe Thereafter, E B decreases slowly

12 Nuclear Stability >260 of nearly 1,700 known nuclides are stable Nuclear stability is the exception, not the rule Most elements have two or more naturally occurring isotopes; some only one Two elements, Tc and Pm have none, which means? Stable plus small number of unstable nuclides = periodic table Chart of the nuclides ( real periodic table )

14 Nuclear Stability Nucleons arranged into regular pattern? Magic numbers concept: combinations of numbers of protons, neutrons, (or both) give certain nuclides unusual stability based on their greater abundance / slower decay rates in the case of unstable nuclides Based on nuclear shell model; paired vs unpaired p or n If p & n shells full, nuclides more tightly bound to nucleus

15 Nuclear Stability Magic numbers for Z and N = 2,8,10,20,28,50,82,126 Ca: magic Z = 20, five stable isotopes, 40 Ca, 42 Ca, 43 Ca, 46 Ca, 48 Ca 40 Ca is doubly magic why?; its abundance is 96.94% 16 O, 17 O, 18 O??? Respective abundances: 99.63%, %, %

16 Giuseppe Oddo (1914) and William Harkins (1917) first report this effect Oddo-Harkins Rule : elements w/even Z more abundant than those w/odd Z

17 Unstable Nuclides If nuclear stability is the exception, not the rule How do we change A? Add or remove particles Addition = fusion Removal = radioactive decay = spontaneous decomposition until a stable nuclear configuration is achieved Produces radionuclides Most known radionuclides do not occur naturally because decay rates are rapid compared to the age of the solar system (extinct)

18 Unstable Nuclides Natural samples contain 266 stable isotopes comprising 81 elements and 65 radioactive isotopes of these comprising 9 additional elements More than 1,650 nuclides and 22 elements, NOT found on Earth, have been synthesized in the laboratory (via?) Probably exist in nature (where?), but we cannot detect (why?)

19 Unstable Nuclides Is it reasonable to expect that a relationship exists between nuclear stability and natural abundances of elements?

22 Radioactive Decay Beta Positron Electron Capture Branched Alpha

23 Radioactive decay changes Z & N Beta decay: Transformation of a neutron into a proton and an electron (Fermi 1934) Electron expelled from nucleus as negatively charged b - particle (negatron) + neutrinos & g rays What happens to Z? N?

24 Partial Chart of the Nuclides isobars isotones isotopes b- decay Parent + daughter have same mass

25 Beta (negatron) decay 40 K 40 Ca +β + ν + Q Where b - = beta particle; ν is the antineutrino; Q = maximum decay energy (1.312 MeV) Nucleus can still be left in an excited state Excess can be emitted as g or transferred from nucleus to extra-nuclear electron e - ejected from its orbital with E k = energy difference between excitation energy of the nucleus and binding energy of the electron Called internal conversion, nucleus can loose energy but no accompanying change in Z or N

26 Metastable Nuclides Some nuclei can remain in metastable excited states for extended lengths of time Called isomers, i.e., nuclear isomers Decay to ground state by g emission or internal conversion Half life (t 1/2 ) = time required for 50% of atoms of particular isotope to decay ranges from s <t 1/2 <241 years 192m Ir (where m denotes isomer) b - decays to 192 Pt (t 1/2 =73 days)

27 Conventional method of displaying overall energy balance of a particular decay process Decay Scheme

28 Positron Decay Large group of radionuclides decay by emission of a positively charged electron = positron from the nucleus Positron emission = transformation of a proton into a neutron, a positron, and a neutrino Thus, Z-1, N+1, A?

29 Positron decay Daughters of parent are?

30 Positron Decay Positron that is emitted in this process is slowed by collisions w/atoms When nearly at rest, it interacts with a normal negative e - ; both are annihilated (1.02 MeV) Their rest masses are converted into two g rays, MeV each Total decay energy = endpoint energy plus 1.02 MeV from annihilation positron neutrino Total energy released by decay 18 F 18 O +β + + ν + Q MeV End-point energy = MeV 1.02 = MeV

31 Positron decay schematic Positron decay can leave the nucleus in an excited state Excess energy lost by emission of gamma rays, e.g., 14 O à 14 N Two sets of b+ emitted; one g observed w/energy of MeV Total decay energy?

32 Negatron vs Positron Decay b - b +

33 Electron Capture Decay Extranuclear electron reacts w/proton in nucleus to form a neutron and a neutrino Probability greatest for K shell electrons (why?) but L & M can also be captured Thus, Z decreases by 1, N increases by 1

34 Branched Decay Mattauch s rule (1934):the difference in atomic number of two stable isobars >1. In other words, two adjacent isobars cannot be stable Why? Because adjacent isobars have different masses and binding energies that makes possible a spontaneous nuclear reaction whereby one isobar is converted into the other by a beta decay that liberates energy This rule implies that two stable isobars must be separated by a radioactive isobar that can undergo a branched decay and therefore form two stable isobaric daughters Examples are 40 Ar, 40 K, and 40 Ca

35 11% of 40 K atoms decay to an excited state of 40 K via e.c. followed by emission of g (1.46 MeV) Another path taken involves 0.16% of 40 K atoms via e.c. directly to ground state of 40 Ar releasing 1.51 MeV Third path taken by only 0.001% of 40 K atoms releases a positron w/endpoint energy of 0.49 MeV followed by annihilation of the positron and release of 2g and 1.02 MeV Branched Decay

36 Other branch leads to formation of 40 Ca to ground state by emission of b - particles w/endpoint energy of 1.32 MeV Note ground-state energy of 40 Ca lies above 40 Ar Other nuclides exhibit branched decay; useful for geological applications Branched Decay

37 Stability Plot for Isobars A = 38 Let s reconsider valley of beta stability; region flanked on either side by radionuclides Many subject to beta decay leading to formation of isobaric daughters that are either closer to or lie within the valley This allows us to draw isobaric energy profiles across the band of nuclides; Consider A = Ar only stable nuclide in this group of isobars Other nuclides decay in such a way that their nuclear configurations are re-arranged until 38 Ar is formed

38 Stability Plot for Isobars A = 38 Let s reconsider valley of beta stability; region flanked on either side by radionuclides Many subject to beta decay leading to formation of isobaric daughters that are either closer to or lie within the valley This allows us to draw isobaric energy profiles across the band of nuclides; Consider A = Ar only stable nuclide in this group of isobars Other nuclides decay in such a way that their nuclear configurations are re-arranged until 38 Ar is formed

39 Stability Plot for Isobars A = 132 Two stable nuclides Separated by unstable 132 Cs and flanked by several other radionuclides belonging to this group of nine isobars

40 Alpha Decay Occurs for nuclides with Z>58 (Ce) and a few w/low Z, e.g., 5 He, 5 Li, and 6 Be Alpha particles = 2 protons and 2 neutrons and carry a +2 charge Z decreases by 2, N decreases by 2, therefore A decreases by 4. The daughter is an isotope of a different element NOT an isobar as was the case for beta decay or e - capture

41 Alpha Decay If Z decreases by 2 & N decrease by 2, what is actually released in the decay reaction? 238 U 234 Th + 4 He + Q a particle Q = total a decay energy Several daughters of U (and Th) can decay by b emission or a decay 227 Ac is third daughter of 235 U Stable 207 Pb is end product after series of a decays

Chem 481 Lecture Material 1/23/09

Chem 481 Lecture Material 1/23/09 Nature of Radioactive Decay Radiochemistry Nomenclature nuclide - This refers to a nucleus with a specific number of protons and neutrons. The composition of a nuclide