Transcript Slide 1

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
3-1
Natural Element Production
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Nuclear Astrophysics

fundamental information on the properties of nuclei and their reactions
to the

perceived properties of astrological objects
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processes that occur in space
Universe is composed of a large variety of massive objects
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distributed in an enormous volume
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Most of the volume is very empty (< 1x10-18 kg/m3) and cold (~ 3 K)
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Massive objects very dense
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(sun's core ~ 2x105 kg/m3) and very hot (sun's core~16x106 K)
At temperatures and densities
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light elements are ionized and have high enough thermal velocities to
induce a nuclear reaction
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heavier elements were created by a variety of nuclear processes in
massive stellar systems
systems must explode to disperse the heavy elements
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distribution of isotopes here on earth
underlying information on the elemental abundances
nuclear processes to produce the primordial elements
3-2
Timeline
• Big bang 15E9 years
ago
• Temperature 1E9 K
• Upon cooling influence
of forces felt

2 hours
 H (89 %)
and He (11
%)
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Strong force for
nucleus
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Electromagnetic
force for
electrons
3-3
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
3-4
•Chart of the
nuclide
trends
•Actinides
some
distance
from stable
elements
3-5
Stable Nuclei
N
Z
Number
even
even
160
odd
even
53
even
odd
49
odd
odd
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• 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
3-6
Origin of element
• Initial H and He
• Others formed from nuclear reactions
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H and He still most abundant
• Noted difference in trends with Z
3-7
Abundances
• General logarithmic decline in the elemental abundance with
atomic number
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a large dip at beryllium (Z=4)
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peaks at carbon and oxygen (Z=6-8), iron (Z ~ 26) and the
platinum (Z=78) to lead (Z=82) region
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a strong odd-even staggering
• All the even Z elements with Z>6 are more abundant than their
odd atomic number neighbors
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nuclear stability
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nearly all radioactive decay will have taken place since
production
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the stable remains and extremely long lived
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isotopic abundances
 strong staggering and gaps
 lightest nuclei mass numbers multiple of 4 have highest
abundances
3-8
Elemental Trends
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Trends are based on isotopes rather than elements
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Isotope described the nucleus composition
 Number of protons and neutrons
 Stability driven by combination of nucleons
3-9
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
3-10
Origin of Elements
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Gravitational coalescence of H and He into clouds
Increase in temperature to fusion
Proton reaction
1H + n → 2H + g
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2H + 1H → 3He
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2H + n → 3H
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3H + 1H → 4He + g
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3He + n → 4He + g
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3H + 2H → 4He + n
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2H + 2H → 4He + g
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4He + 3H → 7Li + g
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3He+4He → 7Be + g
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 7Be short lived
 Initial nucleosynthesis lasted 30 minutes
* Consider neutron reaction and free neutron half life
Further nucleosynthesis in stars
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No EC process in stars
3-11
Stellar Nucleosynthesis
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He burning
4He + 4He ↔ 8Be + γ - 91.78 keV
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 Too short lived
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3 4He → 12C + γ + 7.367 MeV
12C + 4He →16O
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16O + 4He →20Ne
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CNO cycle
12C + 1H →13N + g
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13N →13C + e++ νe
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13C + 1H →14N + γ
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14N + 1H →15O + γ
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15O →15N + e+ + νe
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15N + 1H →12C + 4He
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Net result is conversion of 4
protons to alpha particle
 4 1H → 4He +2 e++ 2 νe +3 γ
3-12
Origin of elements
Neutron Capture and proton
emission
14N + n →14C +1H;
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14N(n,1H)14C
• Alpha Cluster
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Based on behavior of
particles composed of
alphas
• Stability nuclear stability related
to abundance
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Even-even, even A
3-13
Formation of elements A>60
Neutron Capture; S-process
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A>60
68Zn(n, γ) 69Zn, 69Zn → 69Ga + b- + n
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mean times of neutron capture reactions longer than beta decay
half-life
 Isotope can beta decay before another capture
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Up to Bi
3-14
Nucleosynthesis: R process
• Neutron capture time scale very much less than b- decay lifetimes
• Neutron density 1028/m3
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Extremely high flux
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capture times of the order of fractions of a second
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Unstable neutron rich nuclei
• rapidly decay to form stable neutron rich nuclei
• all A<209 and peaks at N=50,82, 126 (magic numbers)
3-15
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P process
Formation of proton rich nuclei
Proton capture process
70<A<200
Photonuclear process, at higher Z (around 40)
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(g, p), (g,a), (g, n)
190Pt and 168Yb from p process
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Also associated with proton capture process (p,g)
Variation on description in the literature
3-16
• Proton-rich nuclei
with Z = 7-26
• (p,g) and b+ decays
that populate the prich 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
rp process (rapid proton
capture)
3-17
Origin of elements
• Binding energy
 Difference
between energy
of nucleus and
nucleons
Related to
mass excess
Dm=mnucleonsmnucleus
Ebind=Dmc2
* Related to
nuclear
models
3-18
Periodic property of element
• Common properties of
elements
• Modern period table
develop
 Actinides added in
1940s by Seaborg
 s, p, d, f blocks
3-19
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

2
d  1
Electron position described by
wavefunction 
x, y, z, and time
Probability of finding electron in
a space proportional to 2
3-20
Bohr Atom
• Net force on the electron is zero
 0=Fdynamic+Fcoulombic
 1/2mev2/r+q1q2/4peor2
Force is 1/r2
E
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Fdr
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)
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3-21
Orbitals
• Wavefunctions specified by
quantum numbers
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n=1,2,3,4
 Principal quantum
number
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l=0 to n-1
 Orbital angular
momentum
 Electron orbitals
* s,p,d,f
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ml= +l
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Spin=+-1/2
 Energy related to Z
and n
* DEtrans=kZ2D(1/n2)
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Orbitals
3-23
Many Electron Atoms
• Electron configuration
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Based on quantum
numbers
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Pauli exclusion principle
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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
3-24
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
3-25
Atomic Radii
• Increase down a group
• Decrease across a period
 Lanthanide and actinide contraction for ionic
radius
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3-27
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
3-28
Study Questions
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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?
3-29
Pop Quiz
• Discuss the reaction necessary for the
formation of 12C in stellar processes. Why is
this unusual?
3-30