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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?