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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

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

Z, atomic number

Neutron

isotopes

Photon

Neutrino

Positron

a particle

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 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

for even A nuclei multiple stable nuclei are possible

no stable heavier odd-odd nuclei

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

strong staggering and gaps

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 composition

Number of protons and neutrons

Stability driven by combination of nucleons

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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

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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

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

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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

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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

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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

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Nucleosynthesis: R process • Neutron capture time scale very much less than b- 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)

(g, p), (g,a), (g, 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,g) and b+ 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 nucleons

Related to mass excess

Dm=mnucleons-mnucleus

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

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

12 d

Electron position described by wavefunction

x, y, z, and time Probability of finding electron in a space proportional to 2

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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)

FdrE

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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)

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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 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

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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

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?