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Nucleosynthesis 8/26/10

Nucleosynthesis 8/26/10. How did the various nuclides originate? What determines their abundance? When were the elements created?. Lecture outline: The age of the universe The Big Bang Nucleosynthesis – initial + stellar Abundance of elements. 900s exposure from Palomar.

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Nucleosynthesis 8/26/10

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  1. Nucleosynthesis 8/26/10 How did the various nuclides originate? What determines their abundance? When were the elements created? • Lecture outline: • The age of the universe • The Big Bang • Nucleosynthesis – initial + stellar • Abundance of elements 900s exposure from Palomar

  2. The Age of the Universe • Four methods of determining age of universe: • Cosmological models – Ho (the Hubble constant – ratio of velocity to distance • in expansion of universe) To=13.7 billion years • 2) Isotope geochemistry – 187Re  187Os, t1/2=40 billion years To=12-17 billion years • 238U decay, t1/2=4.5 billion years To=12.5-16 billion years • 3) Age of oldest star clusters -- measure luminosity • of brightest star, relies on • stellar evolutionary model, • To=11-13 billion years • 4) Oldest white dwarfs -- measure luminosity • of faint white dwarfs to determine • how long they have been cooling, • To=12-13 billion years

  3. The Big Bang - 1920’s: LeMaitre proposes on theoretical grounds that the universe is expanding - 1929: Hubble observed galaxies moving away from us with speeds proportional to distance - 1964: Penzias and Wilson detect ‘primordial static’ left over from Big Bang Time After Big Bang Temperature (K) Event 5.39 x 10-44 s -- appearance of space, time, energy, and superforce 10-43 s 1031 gravity separates 10-35 s 1028 strong force and electro-weak force 10-33 to 10-32 s 1027 inflation 1 x 10-10 s 1015 electromagnetic and weak force 3 x 10-10 to 5 x 10-6 s ~1013 stabilization of quarks, antiquarks 6 x 10-6 1.4 x 1012 formation of protons and neutrons 10s 3.9 x 109 stabilization of electrons and positrons 3.8 m 9 x 108 formation of 2H, 3He, and 4He nuclei 700,000 y 3000 electrons captured by nuclei

  4. WMAP: Wilkinson Microwave Anisotropy Probe age of universe = 13.73 +/- 1% 1992 image microwave radiation from 379,000 years after Big Bang small temperature differences (10-6 K) signify heterogeneous distribution of matter 2005 http://map.gsfc.nasa.gov/

  5. Nucleosynthesis Schematic Nucleosynthetic process Elements created Big bang 1H, 4He, 2H, 3H (Li, B?) Main sequence stars: Hydrogen burning 4He Helium burning 12C, 4He, 24Mg, 16O, 20Ne Carbon burning 24Mg, 23Na, 20Ne CNO cycle 4He x-process (spallation) & supernova (?) Li, Be, B a-process 24Mg, 28Si, 32S, 36Ar, 40Ca e-process 56Fe & other transition s-process up to mass 209 r-process up to mass 254

  6. Nucleosynthesis during the Big Bang - initially, protons (1H) and neutrons combine to form 4He, 2H (D), and 3He via exothermic fusion reactions. - some uncertainty about whether some B, Be, and Li were created at this stage - H & He comprise 99% of mass of universe

  7. Nucleosynthesis during small star evolution - star must form from gravitational accretion of ‘primordial’ H and He - temperature ~ 107 after formation - H-burning creates 4He from 1H, longest stage of star (107 - 1010y) - He-burning begins with formation of Red Giant (T=108) 4He + 4He --> 8Be 8Be + 4He --> 12C 12C + 4He --> 16O and so on to 24Mg - core contracts as He consumed, α-process begins (T=109) 20Ne --> 16O + 4He 20Ne + 4He --> 24Mg and so on to 40Ca For ‘small’ star, such as our Sun

  8. Nucleosynthesis during small star evolution (cont) For ‘small’ star, such as our Sun - odd # masses created by proton bombardment - slow neutron addition (s-process) during late Red Dwarf: 13C + 4He --> 16O + n 21Ne + 4He --> 24Mg + n follows Z/N stability up to mass 209

  9. Nucleosynthesis during supernovae evolution For massive stars - same evolution as for small star, up to Red Giant stage - core contracts and heats at accelerating pace - when T~3x109, several important element- building processes occur: - energetic equilibrium reactions between n, p, and nuclei (e-process), builds up to 56Fe - rapid addition of neutrons (r-process) builds up to mass 254

  10. Heavy element formation - the ‘s’ and ‘r’ processes Neutron # (N)

  11. The abundance of the elements - cosmic - astronomers can detect different elements with spectroscopy (large telescopes equipped with high-resolution spectrometers)

  12. The abundance of the elements - cosmic - the models of nucleosynthesis are driven by the observed relative abundances of the elements in this and other galaxies Magic numbers: 2, 8, 20, 28, 50, 82,126 & even is always better than odd

  13. The abundance of the elements - our solar system Relative composition of heavy elements in sun very similar to “primordial” crust (the carbonaceous chondrite), so we assume that solar system was well-mixed prior to differentiation.

  14. Nuclear Physics & Radioactivity 8/26/10 What holds a nucleus together? What drives radioactive decay? What sets the timescale for radioactive decay? What happens during radioactive decay? • Lecture outline: • nuclear physics • radioactive decay • secular equilibrium • counting statistics a particles in a cloud chamber

  15. The Four Forces of Nature Force Strength Range Occurrence Strong nuclear 1 <<1/r2 (finite, v. short) inter-nucleon Electromagnetic 10-2 1/r2 (infinite, but shielded nucleus, atom Weak nuclear 10-13 <<1/r2 (finite, v. short) B-decay, neutrinos Gravity 10-39 1/r2 (infinite) everywhere Four Tenets of Nuclear Physics 1) mass-energy equivalence (E=mc2) 2) wave-particle duality (particles are waves, and waves are particles) 3) conservation of energy, mass, momentum 4) symmetry

  16. Binding energy Let’s revisit the fusion of four protons to form a 4He nucleus: *these masses come from the table of nuclides We have calculated the mass deficit --> i.e. the whole is less than sum of the parts The mass deficit is represented by a HUGE energy release, which can be calculated using Einstein’s famous equation, E=mc2, and is usually expressed in Mev 56Fe

  17. Contributions to Binding Energy EB = strong nuclear force binding -surface tension binding + spin pairing +shell binding-Coulomb repulsion 1) strong nuclear force -- the more nucleons the better 2) surface tension -- the less surface/volume the better (U better than He) 3) spin pairing -- neutrons and protons have + and - spins, paired spins better 4) shell binding -- nucleus has quantized shells which prefer to be filled (magic numbers) 5) Coulomb repulsion -- packing more protons into nucleus comes at a cost (although neutron addition will stabilize high Z nuclei)

  18. Radioactive Decay - a radioactive parent nuclide decays to a daughter nuclide - the probability that a decay will occur in a unit time is defined as λ (units of y-1) -the decay constant λ is time independent; the mean life is defined as τ=1/λ N0 t1/2 = 5730y 5730

  19. Activity calculations - usually reported in dpm (disintegrations per minute), example: 14C activity = 13.56 dpm / gram C - because activity is linerarly proportional to number N, then A can be substituted for N in the equation Example calculation: How many 14C disintegrations have occurred in a 1g wood sample formed in 1804AD? T=206y t1/2 = 5730y so λ = 0.693/5730y = 1.209e-4 y-1 N0=A0/λ so N0=(13.56dpm*60m/hr*24hr/day*365days/y) /1.209e-4= 5.90e10 atoms N(14C)=N(14C)0*e-(1.209e-4/y)*206y = 5.75e10 atoms # decays = N0-N = 1.5e9 decays

  20. Four types of radioactive decay 1) alpha (α) decay - 4He nucleus (2p + 2n) ejected 2) beta (β) decay - change of nucleus charge, conserves mass 3) gamma (γ) decay - photon emission, no change in A or Z 4) spontaneous fission - for Z=92 and above, generates two smaller nuclei

  21. α decay - involves strong and coloumbic forces - alpha particle and daughter nucleus have equal and opposite momentums (i.e. daughter experiences “recoil”)

  22. β decay - three types 1) β- decay - converts one neutron into a proton and electron - no change of A, but different element - release of anti-neutrino (no charge, no mass) 2) β+ decay - converts one proton into a neutron and electron - no change of A, but different element - release of neutrino 3) Electron capture

  23. γ decay - conversion of strong to coulombic E - no change of A or Z (element) - release of photon - usually occurs in conjunction with other decay Spontaneous fission - heavy nuclides split into two daughters and neutrons - U most common (fission-track dating) Fission tracks from 238U fission in old zircon

  24. 234Th 24d Decay chains and secular equilibrium - three heavy elements feed large decay chains, where decay continues through radioactive daughters until a stable isotope is reached 238U --> radioactive daughters --> 206Pb Also 235U (t1/2)= 700My And 232Th (t1/2)=10By After ~10 half-lives, all nuclides in a decay chain will be in secular equilibrium, where

  25. Decay chains and secular equilibrium (cont) Ex: where l1>>l2 The approach to secular equilibrium is dictated by the intermediary, because the parent is always decaying, and the stable daughter is always accumulating.

  26. Counting Statistics Radioactive decay process behave according to binomial statistics. For large number of decays, binomial statistics approach a perfect Gaussian. Ex: 100 students measure 14C disintegrations in 1g of modern coral (A=13.56dpm) with perfect geiger counters, for 10 minutes 1σ=68.3% 2σ=95% 3σ=99% N+2sqrt(N) N+3sqrt(N) N+sqrt(N) N-3sqrt(N) N-2sqrt(N) N-sqrt(N) Number of Observations Expected value (N) 124.0 135.6 147.2 Observed # disintegrations Since the students only counted 135.6 disintegrations, they will only achieve a 1σ accuracy of ±sqrt(135.6)=±11.6 disintegrations …. Or in relative terms, 11.6d/135.6d = 8.5% In other words, your 1σrelative error (in %) will be equal to (1/(sqrt(total counts)))*100

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