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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Nucleosynthesis8/21/12 How did the various nuclides originate? What determines their abundance? When were the elements created? Lecture outline: 1)The.
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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
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
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
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/
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
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
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
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
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
Heavy element formation - the ‘s’ and ‘r’ processes
Neutron # (N)
Neutron #
Pro
ton
#Chart of the Nuclides, low mass
Entire chart of the nuclides
β decay
EC
α decay
The abundance of the elements - cosmic
- astronomers can detect different elements with spectroscopy (large telescopes equipped with high-resolution spectrometers)
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
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
Unstable nuclides with half lives > 0.5Ma
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
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
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
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)
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
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
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
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.
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