Nucleosynthesis8/21/12 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 – H o (the Hubble constant – ratio of velocity to distance in expansion of universe)T o =13.7 billion years 2)Isotope geochemistry – 187 Re  187 Os, t 1/2 =40 billion years T o =12-17 billion years 238 U decay, t 1/2 =4.5 billion years T o = billion years 3)Age of oldest star clusters -- measure luminosity of brightest star, relies on stellar evolutionary model, T o =11-13 billion years 4)Oldest white dwarfs -- measure luminosity of faint white dwarfs to determine how long they have been cooling, T o =12-13 billion years

The Big Bang ’s: LeMaitre proposes on theoretical grounds that the universe is expanding : Hubble observed galaxies moving away from us with speeds proportional to distance : Penzias and Wilson detect ‘primordial static’ left over from Big Bang Time After Big BangTemperature (K)Event 5.39 x s--appearance of space, time, energy, and superforce s10 31 gravity separates s10 28 strong force and electro-weak force to s10 27 inflation 1 x s10 15 electromagnetic and weak force 3 x to 5 x s~10 13 stabilization of quarks, antiquarks 6 x x formation of protons and neutrons 10s3.9 x 10 9 stabilization of electrons and positrons 3.8 m9 x 10 8 formation of 2H, 3He, and 4He nuclei 700,000 y3000electrons captured by nuclei

image microwave radiation from 379,000 years after Big Bang small temperature differences (10-6 K) signify heterogeneous distribution of matter WMAP: Wilkinson Microwave Anisotropy Probe age of universe = /- 1%

Nucleosynthetic processElements created Big bang 1 H, 4 He, 2 H, 3 H (Li, B?) Main sequence stars: Hydrogen burning 4 He Helium burning 12 C, 4 He, 24 Mg, 16 O, 20 Ne Carbon burning 24 Mg, 23 Na, 20 Ne CNO cycle 4 He x-process (spallation) & supernova (?)Li, Be, B  -process 24 Mg, 28 Si, 32 S, 36 Ar, 40 Ca e-process 56 Fe & other transition s-processup to mass 209 r-processup to mass 254 Nucleosynthesis Schematic

Nucleosynthesis during the Big Bang - initially, protons ( 1 H) and neutrons combine to form 4 He, 2 H (D), and 3 He 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 ~ 10 7 after formation - H-burning creates 4 He from 1 H, longest stage of star ( y) - He-burning begins with formation of Red Giant (T=10 8 K) 4 He + 4 He --> 8 Be 8 Be + 4 He --> 12 C 12 C + 4 He --> 16 O and so on to 24 Mg - core contracts as He consumed,  -process begins (T=10 9 K) 20 Ne --> 16 O + 4 He 20 Ne + 4 He --> 24 Mg and so on to 40 Ca 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: 13 C + 4 He --> 16 O + n 21 Ne + 4 He --> 24 Mg + n follows 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~3x10 9, several important element- building processes occur: - energetic equilibrium reactions between n, p, and nuclei (e-process), builds up to 56 Fe - rapid addition of neutrons (r-process) builds up to mass 254

Heavy element formation - the ‘s’ and ‘r’ processes Neutron # (N)

Neutron # Proton # 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 & Radioactivity8/21/12 What holds a nucleus together? What drives radioactive decay? What sets the timescale for radioactive decay? 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 ForceStrengthRangeOccurrence Strong nuclear1<<1/r 2 (finite, v. short)inter-nucleon Electromagnetic /r 2 (infinite, but shieldednucleus, atom Weak nuclear <<1/r 2 (finite, v. short)B-decay, neutrinos Gravity /r 2 (infinite)everywhere Four Tenets of Nuclear Physics 1) mass-energy equivalence (E=mc 2 ) 2) wave-particle duality (particles are waves, and waves are particles) 3) conservation of energy, mass, momentum 4) symmetry

Binding energy Let’s revisit the fusion of four protons to form a 4 He nucleus: *these masses come from 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 calculated using Einstein’s famous equation, E=mc 2, and is usually expressed in Mev 56 Fe

Contributions to Binding Energy E B = strong nuclear force binding -surface tension binding + spin pairing +shell binding-Coulomb repulsion 1) strong nuclear force -- the more nucleons the better 2) surface tension -- the less surface/volume the better (U better than He) 3) spin pairing -- neutrons and protons have + and - spins, paired spins better 4) 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  (units of y -1 ) -  the decay constant  is time independent; the mean life is defined as  =1/λ t 1/2 = 5730y 5730 N0N0

Activity calculations - usually reported in dpm (disintegrations per minute), example: 14 C activity = dpm / gram C - because activity is linerarly proportional to number N, then A can be substituted for N in the equation Example calculation: How many 14 C disintegrations have occurred in a 1g wood sample formed in 1804AD? T=208y t 1/2 = 5730y so  = 0.693/5730y = 1.209e -4 y -1 N 0 =A 0 /λ so N 0 =(13.56dpm*60m/hr*24hr/day*365days/y) /1.209e -4 = 5.90e 10 atoms N( 14 C)=N( 14 C) 0 *e -(1.209e-4/y)*208y = 5.75e 10 atoms # decays = N 0 -N = 1.46e 9 decays

Four types of radioactive decay 1) alpha (  ) decay - 4 He nucleus (2p + 2n) ejected 2) beta (  ) decay - change of nucleus charge, conserves mass 3) gamma (  ) decay - photon emission, no change in A or Z 4) spontaneous fission - for Z=92 and above, generates two smaller nuclei

 decay - involves strong and coloumbic forces - alpha particle and daughter nucleus have equal and opposite momentums (i.e. daughter experiences “recoil”)

 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

 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 238 U fission in old zircon - heavy nuclides split into two daughters and neutrons - U most common (fission-track dating)

Decay chains and secular equilibrium - three heavy elements feed large decay chains, where decay continues through radioactive daughters until a stable isotope is reached 238 U --> radioactive daughters --> 206 Pb Also 235 U (t 1/2 )= 700My And 232 Th (t 1/2 )=10By After ~10 half-lives, all nuclides in a decay chain will be in secular equilibrium, where 234 Th 24d

Decay chains and secular equilibrium (cont) Ex: where 1 >> 2 The approach to secular equilibrium is dictated by the intermediary, because the parent is always decaying, and the stable daughter is always accumulating.

Counting Statistics Radioactive decay process behave according to binomial statistics. For large number of decays, binomial statistics approach a perfect Gaussian. Observed # disintegrations Number of Observations Ex: 100 students measure 14 C disintegrations in 1g of modern coral (A=13.56dpm) with perfect geiger counters, for 10 minutes Expected value (N) N+sqrt(N) N-sqrt(N) N+2sqrt(N) N-2sqrt(N) N+3sqrt(N) N-3sqrt(N) 1  =68.3% 2  =95% 3  =99% Since the students only counted disintegrations, they will only achieve a 1  accuracy of ±sqrt(135.6)=±11.6 disintegrations …. Or in relative terms, 11.6d/135.6d = 8.5% In other words, your 1  relative error (in %) will be equal to (1/(sqrt(total counts)))*100