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Lecture 2 Nucleosynthesis

Lecture 2 Nucleosynthesis. Reading: Nuclear and Radiochemistry: Chapter 13 Modern Nuclear Chemistry : Chapter 12 Formation processes Role of nuclear reactions Different areas of chart of nuclides Relationship between nuclear properties and chemical abundance Electron orbitals.

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Lecture 2 Nucleosynthesis

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  1. Lecture 2 Nucleosynthesis • Reading: • Nuclear and Radiochemistry: Chapter 13 • Modern Nuclear Chemistry: Chapter 12 • Formation processes • Role of nuclear reactions • Different areas of chart of nuclides • Relationship between nuclear properties and chemical abundance • Electron orbitals

  2. Natural Element Production Nuclear Astrophysics fundamental information on the properties of nuclei and their reactions to the perceived properties of astrological objects processes that occur in space Universe is composed of a large variety of massive objects distributed in an enormous volume Most of the volume is very empty (< 1x10-18 kg/m3) and cold (~ 3 K) Massive objects very dense (sun's core ~ 2x105 kg/m3) and very hot (sun's core~16x106 K) At temperatures and densities light elements are ionized and have high enough thermal velocities to induce a nuclear reaction heavier elements were created by a variety of nuclear processes in massive stellar systems systems must explode to disperse the heavy elements distribution of isotopes here on earth underlying information on the elemental abundances nuclear processes to produce the primordial elements

  3. Timeline • Big bang 15E9 years ago • Temperature 1E9 K • Upon cooling influence of forces felt • 2 hours • H (89 %) and He (11 %) • Strong force for nucleus • Electromagnetic force for electrons

  4. Subatomic particles • A number of subatomic particles have relevance to radiochemistry • Electron • Proton • Z, atomic number • Neutron • isotopes • Photon • Neutrino • Positron • aparticle • Is actually a nucleus • b particle

  5. Chart of the nuclide trends • Actinides some distance from stable elements

  6. Stable Nuclei N even odd even odd Z even even odd odd Number 160 53 49 4 • As Z increases the line of stability moves from N=Z to N/Z ~ 1.5 • influence of the Coulomb force. For odd A nuclei • only one stable isobar is found while for even A nuclei • no stable heavier odd-odd nuclei • Find the stable odd-odd nuclei

  7. Origin of element • Initial H and He • Others formed from nuclear reactions • H and He still most abundant • Noted difference in trends with Z

  8. Abundances • General logarithmic decline in the elemental abundance with atomic number • a large dip at beryllium (Z=4) • peaks at carbon and oxygen (Z=6-8), iron (Z ~ 26) and the platinum (Z=78) to lead (Z=82) region • a strong odd-even staggering • All the even Z elements with Z>6 are more abundant than their odd atomic number neighbors • nuclear stability • nearly all radioactive decay will have taken place since production • the stable remains and extremely long lived • isotopic abundances • strong staggering and gaps • lightest nuclei mass numbers multiple of 4 have highest abundances

  9. Elemental Trends • Trends are based on isotopes rather than elements • Isotope described the nucleus composition • Number of protons and neutrons • Stability driven by combination of nucleons

  10. Abundances • Earth predominantly • oxygen, silicon, aluminum, iron and calcium • more than 90% of the earth’s crust • Solar system is mostly hydrogen • some helium • Based on mass of sun • Geophysical and geochemical material processing

  11. Origin of Elements • Gravitational coalescence of H and He into clouds • Increase in temperature to fusion • Proton reaction • 1H + n → 2H + g • 2H + 1H → 3He • 2H + n → 3H • 3H + 1H → 4He + g • 3He + n → 4He + g • 3H + 2H → 4He + n • 2H + 2H → 4He + g • 4He + 3H → 7Li + g • 3He+3He → 7Be+ g • 7Be short lived • Initial nucleosynthesis lasted 30 minutes • Consider neutron reaction and free neutron half life • Further nucleosynthesis in stars • No EC process in stars

  12. Stellar Nucleosynthesis • He burning • 4He+ 4He ↔ 8Be + γ - 91.78 keV • Too short lived • 3 4He → 12C + γ + 7.367 MeV • 12C + 4He →16O • 16O + 4He →20Ne • CNO cycle • 12C + 1H →13N + g • 13N →13C + e++ νe • 13C + 1H →14N + γ • 14N + 1H →15O + γ • 15O →15N + e+ + νe • 15N + 1H →12C + 4He • Net result is conversion of 4 protons to alpha particle • 4 1H → 4He +2 e++ 2 νe +3 γ

  13. Origin of elements Neutron Capture and proton emission • 14N + n →14C +1H; 14N(n,1H)14C • Alpha Cluster • Based on behavior of particles composed of alphas • Stability nuclear stability related to abundance • Even-even, even A

  14. Formation of elements A>60 Neutron Capture; S-process • A>60 • 68Zn(n, γ) 69Zn, 69Zn → 69Ga+ b- + n • mean times of neutron capture reactions longer than beta decay half-life • Isotope can beta decay before another capture • Up to Bi

  15. Nucleosynthesis: R process • Neutron capture time scale very much less than - decay lifetimes • Neutron density 1028/m3 • Extremely high flux • capture times of the order of fractions of a second • Unstable neutron rich nuclei • rapidly decay to form stable neutron rich nuclei • all A<209 and peaks at N=50,82, 126 (magic numbers)

  16. P process • Formation of proton rich nuclei • 70<A<200 • Photonuclear process, and also couple with positron decay • (, p), (,), (, n) • 190Pt and 168Yb from p process

  17. rp process (rapid photon capture) • Proton-rich nuclei with Z = 7-26 • (p,) and + decays that populate the p-rich nuclei • Initiates as a side chain of the CNO cycle • 21Na and 19Ne • Forms a small number of nuclei with A< 100

  18. Origin of elements • Binding energy • Difference between energy of nucleus and nucleons • Related to mass excess • Dm=mnucleons-mnucleus • Ebind=Dmc2 • Related to nuclear models

  19. Periodic property of element • Common properties of elements • Modern period table develop • Actinides added in 1940s by Seaborg • s, p, d, f blocks

  20. Hydrogenic atoms • Atoms with only one electron • Simplifies calculations • Electron position described by wavefunction y • x, y, z, and time • Probability of finding electron in a space proportional to y2

  21. Bohr Atom • Models of atoms • Plum pudding • Bohr atom • Inclusion of quantum states • Based on Rutherford atom • Bohr atom for 1 electron system • Etotal =1/2mev2+q1q2/4peor • q2=-e • Include proton and electron • 1/2mev2-Ze2/4peor

  22. Bohr Atom • Net force on the electron is zero • 0=Fdynamic+Fcoulombic • 1/2mev2/r+q1q2/4peor2 • Force is 1/r2 • Energy 1/r • 1/2mev2/r-Ze2/4peor2 • Z is charge on nucleus • Quantize energy through angular momentum • mvr=nh/2p, n=1,2,3…. • Can solve for r, E, v • R=(eoh2/pmee2)(n2/Z) • Radius is quantized and goes at n2 • R=0.529 Å for Z=1, n=1 • Ao (Bohr radius)

  23. Orbitals • Wavefunctions specified by quantum numbers • n=1,2,3,4 • Principal quantum number • l=0 to n-1 • Orbital angular momentum • Electron orbitals • s,p,d,f • ml= +l • Spin=+-1/2 • Energy related to Z and n • DEtrans=-kZ2D(1/n2)

  24. Orbitals

  25. Atomic Spectra • Quantum numbers • n=1,2,3,4 • r=aon2/Z for gases with 1 electron • Energy • E=-(mee4/8eo2h2)Z2/n2 • For ground state H • E=2.18E-18 J/atom=k • Can determine J/mole 1312 kJ/mole • Energy goes as –k/n2 • System converges to limit

  26. Energy • n=infinity, r=infinity , E=0, unbound e- • Ionization energy • k is ionization energy • Velocity • v=nh/2pmer • Ionization energy • Minimum energy required to remove electron from atom in gas phase • Multiple ionization energies

  27. Many Electron Atoms • Electron configuration • Based on quantum numbers • Pauli exclusion principle • Aufbau principle and Hund’s rule • Degenerate orbitals have same spin • Maximize unfilled orbitals • 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f

  28. Many electron orbitals • Electron configuration of Zr and Zr4+ • [Kr]4d25s2 and [Kr] • For Fe, Fe2+, and Fe3+ • [Ar]4s23d6, [Ar]4s23d4, [Ar]4s23d3 • Effective nuclear charge • Zeff=Z-s • Related to electron penetration towards nucleus

  29. Effective Nuclear Charge

  30. Atomic Radii • Increase down a group • Decrease across a period • Lanthanide and actinide contraction for ionic radius

  31. Topic review • Routes and reactions in nucleosynthesis • Influence of reaction rate and particles on nucleosynthesis • Relationships between nuclear and chemical properties • Electron orbitals and interactions

  32. Study Questions • How are actinides made in nucleosynthesis? • What is the s-process? • What elements were produced in the big bang? • Which isotopes are produced by photonuclear reactions? • What do binding energetic predict about abundance and energy release? • What are the stable odd-odd isotopes?

  33. Pop Quiz • Discuss the reaction necessary for the formation of 12C in stellar processes. Why is this unusual?

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