3-1 rdch 702: nucleosynthesis readings: §modern nuclear chemistry: chapter 12 nuclear astrophysics,...
TRANSCRIPT
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RDCH 702: Nucleosynthesis
• Readings:§ Modern Nuclear Chemistry: Chapter 12
Nuclear Astrophysics, Chapter 2 Nuclear Properties
• Formation processes§ Role of nuclear reactions
• Relationship between nuclear properties and chemical abundance
• Electron orbitals
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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
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Timeline
• Big bang 15E9 years ago
• Temperature 1E9 K• Upon cooling influence
of forces felt§ 2 hours
à H (89 %) and He (11 %)
§ Strong force for nucleus
§ Electromagnetic force for electrons
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Subatomic particles
• A number of subatomic particles have relevance to radiochemistry§ Electron§ Proton
à Z, atomic number§ Neutron
à isotopes§ Photon§ Neutrino§ Positron§ a particle
à Is actually a nucleus§ b particle
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• Chart of the nuclide trends• Actinides
some distance from stable elements
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Stable Nuclei
N even odd even oddZ even even odd oddNumber 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 § for even A nuclei multiple stable nuclei are
possible§ no stable heavier odd-odd nuclei
à Find the stable odd-odd nuclei
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Origin of element
• Initial H and He• Others formed from nuclear reactions
§ H and He still most abundant• Noted difference in trends with Z
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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
à strong staggering and gapsà lightest nuclei mass numbers multiple of 4 have highest
abundances
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Elemental Trends• Trends are based on isotopes rather than elements
§ Isotope described the nucleus compositionà Number of protons and neutronsà Stability driven by combination of nucleons
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Abundances• Earth predominantly
§ oxygen, silicon, aluminum, iron and calciumà 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
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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+4He → 7Be + g
à 7Be short livedà Initial nucleosynthesis lasted 30 minutes
* Consider neutron reaction and free neutron half life• Further nucleosynthesis in stars
§ No EC process in stars
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Stellar Nucleosynthesis• He burning
§ 4He + 4He ↔ 8Be + γ - 91.78 keV à 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 particleà 4 1H → 4He +2 e++ 2 νe +3 γ
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Origin of elementsNeutron 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
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Formation of elements A>60Neutron Capture; S-process
§ A>60§ 68Zn(n, γ) 69Zn, 69Zn → 69Ga + b- + n§ mean times of neutron capture reactions longer than beta decay
half-lifeà Isotope can beta decay before another capture
§ Up to Bi
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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)
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P process• Formation of proton rich nuclei• Proton capture process• 70<A<200• Photonuclear process, at higher Z (around 40)
§ (, p), (,), (, n)§ 190Pt and 168Yb from p process
• Also associated with proton capture process (p,g)• Variation on description in the literature
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rp process (rapid proton capture)
• Proton-rich nuclei with Z = 7-26
• (p,) and + decays that populate the p-rich nuclei§ Also associated
with rapid proton capture process
• Initiates as a side chain of the CNO cycle § 21Na and 19Ne
• Forms a small number of nuclei with A< 100
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Origin of elements
• Binding energy§ Difference
between energy of nucleus and nucleonsà Related to
mass excess
à Dm=mnucleons-mnucleus
à Ebind=Dmc2
* Related to nuclear models
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Periodic property of element
• Common properties of elements
• Modern period table develop § Actinides added in
1940s by Seaborg§ s, p, d, f blocks
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Bohr Atom
• Models of atoms§ Plum pudding§ Bohr atom
à Inclusion of quantum states
àBased on Rutherford atom• Bohr atom for 1 electron system
§ Etotal =1/2mev2+q1q2/4peor
àq2=-e
* Include proton and electron
§ 1/2mev2-Ze2/4peor
12 dElectron position described by wavefunction y
x, y, z, and timeProbability of finding electron in a space proportional to y2
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Bohr Atom• Net force on the electron is zero
§ 0=Fdynamic+Fcoulombic
§ 1/2mev2/r+q1q2/4peor2
àForce is 1/r2
àEnergy 1/r
§ 1/2mev2/r-Ze2/4peor2
àZ is charge on nucleus• Quantize energy through angular momentum
§ mvr=nh/2 , p n=1,2,3….àCan 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
àAo (Bohr radius)
FdrE
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Orbitals
• Wavefunctions specified by quantum numbers§ n=1,2,3,4
à Principal quantum number
§ l=0 to n-1à Orbital angular
momentumà Electron orbitals
* s,p,d,f§ ml= +l§ Spin=+-1/2
à Energy related to Z and n* DEtrans
=-kZ2D(1/n2)
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Orbitals
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Many Electron Atoms
• Electron configuration§ Based on quantum
numbers§ Pauli exclusion
principle§ Aufbau principle and
Hund’s ruleà Degenerate orbitals
have same spinà Maximize unfilled
orbitals* 1s 2s 2p 3s 3p 4s
3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f
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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
à Related to electron penetration towards nucleus
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Atomic Radii
• Increase down a group• Decrease across a period
§ Lanthanide and actinide contraction for ionic radius
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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
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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?
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Pop Quiz
• Discuss the reaction necessary for the formation of 12C in stellar processes. Why is this unusual?