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![Page 1: Nucleosynthesis8/21/12 How did the various nuclides originate? What determines their abundance? When were the elements created? Lecture outline: 1)The.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d095503460f949db44f/html5/thumbnails/1.jpg)
Nucleosynthesis 8/21/12
How did the various nuclides originate?
What determines their abundance?
When were the elements created?
Lecture outline:1) The age of the universe
2) The Big Bang
3) Nucleosynthesis – initial + stellar
4) Abundance of elements
900s exposure from Palomar
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The Age of the Universe
Four methods of determining age of universe:
1) Cosmological models – Ho (the Hubble constant – ratio of velocity to distancein expansion of universe) To=13.7 billion years
2) Isotope geochemistry – 187Re 187Os, t1/2=40 billion years To=12-17 billion years238U decay, t1/2=4.5 billion years To=12.5-16 billion years
3) Age of oldest star clusters -- measure luminosity of brightest star, relies on stellar evolutionary model, To=11-13 billion years
4) Oldest white dwarfs -- measure luminosity of faint white dwarfs to determinehow long they have been cooling, To=12-13 billion years
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The Big Bang
- 1920’s: LeMaitre proposes on theoretical grounds that the universe is expanding
- 1929: Hubble observed galaxies moving away from us with speeds proportional to distance
- 1964: Penzias and Wilson detect ‘primordial static’ left over from Big Bang
Time After Big Bang Temperature (K) Event
5.39 x 10-44 s -- appearance of space, time, energy,and superforce
10-43 s 1031 gravity separates10-35 s 1028 strong force and electro-weak force10-33 to 10-32 s 1027 inflation1 x 10-10 s 1015 electromagnetic and weak force3 x 10-10 to 5 x 10-6 s ~1013 stabilization of quarks, antiquarks6 x 10-6 1.4 x 1012 formation of protons and neutrons10s 3.9 x 109 stabilization of electrons and positrons3.8 m 9 x 108 formation of 2H, 3He, and 4He nuclei700,000 y 3000 electrons captured by nuclei
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1992
2005
image microwaveradiation from 379,000 years after Big Bang
small temperaturedifferences (10-6 K)signify heterogeneousdistribution of matter
WMAP:Wilkinson Microwave Anisotropy Probe
age of universe =13.73 +/- 1%
http://map.gsfc.nasa.gov/
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Nucleosynthetic process Elements created
Big bang 1H, 4He, 2H, 3H (Li, B?)
Main sequence stars:
Hydrogen burning 4He
Helium burning 12C, 4He, 24Mg, 16O, 20Ne
Carbon burning 24Mg, 23Na, 20Ne
CNO cycle 4He
x-process (spallation)& supernova (?) Li, Be, B
-process 24Mg, 28Si, 32S, 36Ar, 40Ca
e-process 56Fe & other transition
s-process up to mass 209
r-process up to mass 254
Nucleosynthesis Schematic
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Nucleosynthesis during the Big Bang
- initially, protons (1H) and neutrons combine to form 4He, 2H (D), and 3He via exothermic fusion reactions.
- some uncertainty about whether some B, Be, and Li were created at this stage
- H & He comprise 99% of mass of universe
![Page 7: Nucleosynthesis8/21/12 How did the various nuclides originate? What determines their abundance? When were the elements created? Lecture outline: 1)The.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649d095503460f949db44f/html5/thumbnails/7.jpg)
Nucleosynthesis during small star evolution
- star must form from gravitational accretion of ‘primordial’ H and He
- temperature ~ 107 after formation
- H-burning creates 4He from 1H, longest stage of star (107 - 1010y)
- He-burning begins with formation of Red Giant (T=108K)
4He + 4He --> 8Be8Be + 4He --> 12C12C + 4He --> 16O and so on to 24Mg
- core contracts as He consumed, -process begins (T=109K)
20Ne --> 16O + 4He20Ne + 4He --> 24Mg and so on to 40Ca
For ‘small’ star, such as our Sun
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Nucleosynthesis during small star evolution (cont)
For ‘small’ star, such as our Sun
- odd # masses created by proton bombardment
- slow neutron addition (s-process) during late Red Dwarf:13C + 4He --> 16O + n21Ne + 4He --> 24Mg + nfollows Z/N stability up to mass 209
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Nucleosynthesis during supernovae evolution
For massive stars- same evolution as for small star, up to Red Giant stage
- core contracts and heats at accelerating pace
- when T~3x109, several important element- building processes occur:
- energetic equilibrium reactions between n, p, and nuclei (e-process), builds up to 56Fe
- rapid addition of neutrons (r-process) builds up to mass 254
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Heavy element formation - the ‘s’ and ‘r’ processes
Neutron # (N)
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Neutron #
Pro
ton
#Chart of the Nuclides, low mass
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Entire chart of the nuclides
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β decay
EC
α decay
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The abundance of the elements - cosmic
- astronomers can detect different elements with spectroscopy (large telescopes equipped with high-resolution spectrometers)
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Magic numbers: 2, 8, 20, 28, 50, 82,126
& even is always better than odd
The abundance of the elements - cosmic
- the models of nucleosynthesis are driven by the observed relative abundances of the elements in this and other galaxies
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Relative composition of heavy elements in sun very similar to “primordial”crust (the carbonaceous chondrite), so we assume that solar system was well-mixed prior to differentiation.
The abundance of the elements - our solar system
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Unstable nuclides with half lives > 0.5Ma
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Nuclear Physics & Radioactivity 8/21/12
What holds a nucleus together?
What drives radioactive decay?
What sets the timescale for radioactivedecay?
What happens during radioactive decay?
Lecture outline:1) nuclear physics
2) radioactive decay
3) secular equilibrium
4) counting statistics
particles in a cloud chamber
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The Four Forces of Nature
Force Strength Range Occurrence
Strong nuclear 1 <<1/r2 (finite, v. short) inter-nucleon
Electromagnetic 10-2 1/r2 (infinite, but shielded nucleus, atom
Weak nuclear 10-13 <<1/r2 (finite, v. short) B-decay,neutrinos
Gravity 10-39 1/r2 (infinite) everywhere
Four Tenets of Nuclear Physics
1) mass-energy equivalence (E=mc2)2) wave-particle duality (particles are waves, and waves are particles)3) conservation of energy, mass, momentum4) symmetry
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Binding energyLet’s revisit the fusion of four protons to form a 4He nucleus:
1 41 24( ) 1( ) 2 2
4(1.007277) 1(4.00150)
0.02761
eH He e E
m
m amu
*these masses comefrom the table of nuclides
We have calculated the mass deficit --> i.e. the whole is less than sum of the parts
The mass deficit is represented by a HUGE energy release, which can be calculatedusing Einstein’s famous equation, E=mc2, and is usually expressed in Mev
56F
e
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Contributions to Binding Energy
EB = strong nuclear force binding -surface tension binding + spin pairing+shell binding-Coulomb repulsion
1) strong nuclear force -- the more nucleons the better2) surface tension -- the less surface/volume the better (U better than He)3) spin pairing -- neutrons and protons have + and - spins, paired spins better4) shell binding -- nucleus has quantized shells which prefer to be filled (magic numbers)5) Coulomb repulsion -- packing more protons into nucleus comes at a cost (although
neutron addition will stabilize high Z nuclei)
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Radioactive Decay- a radioactive parent nuclide decays to a daughter nuclide
- the probability that a decay will occur in a unit time is defined as λ(units of y-1)
-the decay constant λ is time independent; the mean life is defined as τ=1/λ
0
100000
200000
300000
400000
500000
600000
700000
800000
900000
1000000
0 10000 20000 30000 40000 50000
Years
Nu
mb
er o
f 14
C a
tom
s
dNN
dtλ
0tN N e λ
t1/2 = 5730y
5730
N0
1/ 2
ln(2)
tλ
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Activity calculations
- usually reported in dpm (disintegrations per minute), example: 14C activity = 13.56 dpm / gram C
Activity Nλ
0tA A e λ - because activity is linerarly proportional to number N,
then A can be substituted for N in the equation 0tN N e λ
Example calculation:
How many 14C disintegrations have occurred in a 1g wood sample formed in 1804AD?
T=208y
t1/2 = 5730y so λ = 0.693/5730y = 1.209e-4 y-1
N0=A0/λ so N0=(13.56dpm*60m/hr*24hr/day*365days/y) /1.209e-4= 5.90e10 atoms
N(14C)=N(14C)0*e-(1.209e-4/y)*208y = 5.75e10 atoms
# decays = N0-N = 1.46e9 decays
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Four types of radioactive decay
1) alpha () decay - 4He nucleus (2p + 2n) ejected2) beta (β) decay - change of nucleus charge, conserves mass3) gamma (γ) decay - photon emission, no change in A or Z4) spontaneous fission - for Z=92 and above, generates two smaller nuclei
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decay
- involves strong and coloumbic forces- alpha particle and daughter nucleus have equal and opposite momentums
(i.e. daughter experiences “recoil”)
241 237 495 93 2Am Np He
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β decay - three types
- converts one neutron into a proton and electron- no change of A, but different element- release of anti-neutrino (no charge, no mass)
1) β- decay
2) β+ decay
3) Electron capture
- converts one proton into a neutron and electron- no change of A, but different element- release of neutrino
- converts one proton into a neutron - no change of A, but different element- release of neutrino
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γ decay
- conversion of strong to coulombic E- no change of A or Z (element)- release of photon- usually occurs in conjunction with other decay
Spontaneous fission
Fission tracks from 238U fission in old zircon
- heavy nuclides split into two daughtersand neutrons
- U most common (fission-track dating)
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Decay chains and secular equilibrium
- three heavy elements feed large decay chains, where decay continues through radioactive daughters until a stable isotope is reached
238U --> radioactive daughters --> 206PbAlso 235U (t1/2)= 700MyAnd 232Th (t1/2)=10By
After ~10 half-lives, all nuclides in a decay chain will be in secular equilibrium, where
1 2( ) ( ) ( ) ...Activity P A D A D
234Th24d
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Decay chains and secular equilibrium (cont)
Ex:
where λ1>>λ2
t/ τ1
λ1/ λ2=0.1
0.001
0.01
0.1
1
0 1 2 3 4 5
N/N
1o (
log
sca
le) N1
N2
N3
secular equilibriumλ1N
1=λ2N2
5τ2
2
N2o=0
N2o=N
1o
The approach to secular equilibrium is dictated by the intermediary, because the parent is always decaying, and the stable daughter is always accumulating.
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Counting StatisticsRadioactive decay process behave according to binomial statistics.For large number of decays, binomial statistics approach a perfect Gaussian.
Observed # disintegrations
Num
ber
of O
bser
vatio
ns
Ex: 100 students measure 14C disintegrations in 1g of modern coral (A=13.56dpm)with perfect geiger counters, for 10 minutes
135.6
Ex
pe
cte
d v
alu
e (
N)
N+
sqrt
(N)
N-s
qrt
(N)
N+
2sq
rt(N
)
N-2
sqrt
(N)
N+
3sq
rt(N
)
N-3
sqrt
(N) 1σ=68.3%
2σ=95%3σ=99%
147.2124.0
Since the students only counted 135.6 disintegrations, they will only achieve a 1σ accuracyof ±sqrt(135.6)=±11.6 disintegrations …. Or in relative terms, 11.6d/135.6d = 8.5%
In other words, your 1σ relative error (in %) will be equal to (1/(sqrt(total counts)))*100