3-1 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

3-2 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 (< 1x kg/m3) and cold (~ 3 K) §Massive objects very dense §(sun's core ~ 2x10 5 kg/m3) and very hot (sun's core~16x10 6 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

3-3 Timeline Big bang 15E9 years ago Temperature 1E9 K Upon cooling influence of forces felt §2 hours àH (89 %) and He (11 %) §Strong force for nucleus §Electromagnetic force for electrons

3-4 Subatomic particles A number of subatomic particles have relevance to radiochemistry §Electron §Proton àZ, atomic number §Neutron àisotopes §Photon §Neutrino §Positron   particle àIs actually a nucleus   particle

3-5 Chart of the nuclide trends Actinides some distance from stable elements

3-6 Stable Nuclei Nevenoddevenodd Z even even odd odd Number 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 àFind the stable odd-odd nuclei

3-7 Origin of element Initial H and He Others formed from nuclear reactions §H and He still most abundant Noted difference in trends with Z

3-8 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 àstrong staggering and gaps àlightest nuclei mass numbers multiple of 4 have highest abundances

3-9 Elemental Trends Trends are based on isotopes rather than elements §Isotope described the nucleus composition àNumber of protons and neutrons àStability driven by combination of nucleons

3-10 Abundances Earth predominantly §oxygen, silicon, aluminum, iron and calcium àmore than 90% of the earth’s crust Solar system is mostly hydrogen §some helium §Based on mass of sun Geophysical and geochemical material processing

3-11 Origin of Elements Gravitational coalescence of H and He into clouds Increase in temperature to fusion Proton reaction  1 H + n → 2 H +  § 2 H + 1 H → 3 He § 2 H + n → 3 H  3 H + 1 H → 4 He +   3 He + n → 4 He +  § 3 H + 2 H → 4 He + n  2 H + 2 H → 4 He +   4 He + 3 H → 7 Li +   3 He+ 4 He → 7 Be +  à 7 Be short lived àInitial nucleosynthesis lasted 30 minutes *Consider neutron reaction and free neutron half life Further nucleosynthesis in stars §No EC process in stars

3-12 Stellar Nucleosynthesis He burning § 4 He + 4 He ↔ 8 Be + γ keV àToo short lived §3 4 He → 12 C + γ MeV § 12 C + 4 He → 16 O § 16 O + 4 He → 20 Ne CNO cycle  12 C + 1 H → 13 N +  § 13 N → 13 C + e + + νe § 13 C + 1 H → 14 N + γ § 14 N + 1 H → 15 O + γ § 15 O → 15 N + e + + νe § 15 N + 1 H → 12 C + 4 He §Net result is conversion of 4 protons to alpha particle à4 1 H → 4 He +2 e νe +3 γ

3-13 Origin of elements Neutron Capture and proton emission § 14 N + n → 14 C + 1 H; 14 N(n, 1 H) 14 C Alpha Cluster §Based on behavior of particles composed of alphas Stability nuclear stability related to abundance §Even-even, even A

3-14 Formation of elements A>60 Neutron Capture; S-process §A>60  68 Zn(n, γ) 69 Zn, 69 Zn → 69 Ga +    §mean times of neutron capture reactions longer than beta decay half-life àIsotope can beta decay before another capture §Up to Bi

3-15 Nucleosynthesis: R process Neutron capture time scale very much less than  - decay lifetimes Neutron density /m 3 §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)

3-16 P process Formation of proton rich nuclei Proton capture process 70<A<200 Photonuclear process, at higher Z (around 40)  ( , p), ( ,  ), ( , n) § 190 Pt and 168 Yb from p process Also associated with proton capture process (p,  ) Variation on description in the literature

3-17 rp process (rapid proton capture) Proton-rich nuclei with Z = 7-26 (p,  ) and  + decays that populate the p- rich nuclei §Also associated with rapid proton capture process Initiates as a side chain of the CNO cycle § 21 Na and 19 Ne Forms a small number of nuclei with A< 100

3-18 Origin of elements Binding energy §Difference between energy of nucleus and nucleons àRelated to mass excess   m=m nucleons - m nucleus  E bind =  mc 2 *Related to nuclear models

3-19 Periodic property of element Common properties of elements Modern period table develop §Actinides added in 1940s by Seaborg §s, p, d, f blocks

3-20 Bohr Atom Models of atoms §Plum pudding §Bohr atom àInclusion of quantum states àBased on Rutherford atom Bohr atom for 1 electron system  E total =1/2m e v 2 +q 1 q 2 /4   r àq 2 =-e *Include proton and electron  1/2m e v 2 -Ze 2 /4   r Electron position described by wavefunction  x, y, z, and time Probability of finding electron in a space proportional to  

3-21 Bohr Atom Net force on the electron is zero §0=F dynamic +F coulombic  1/2m e v 2 /r+q 1 q 2 /4   r 2 àForce is 1/r 2 àEnergy 1/r  1/2m e v 2 /r-Ze 2 /4   r 2 àZ is charge on nucleus Quantize energy through angular momentum  mvr=nh/2  n=1,2,3…. àCan solve for r, E, v R=(   h 2 /  m e e 2 )(n 2 /Z) §Radius is quantized and goes at n 2 §R=0.529 Å for Z=1, n=1 à A o (Bohr radius)

3-22 Orbitals Wavefunctions specified by quantum numbers §n=1,2,3,4 àPrincipal quantum number §l=0 to n-1 àOrbital angular momentum àElectron orbitals *s,p,d,f §m l = +l §Spin=+-1/2 àEnergy related to Z and n *  E trans = - kZ 2  (1/n 2 )

3-23 Orbitals

3-24 Many Electron Atoms Electron configuration §Based on quantum numbers §Pauli exclusion principle §Aufbau principle and Hund’s rule àDegenerate orbitals have same spin àMaximize unfilled orbitals *1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f

3-25 Many electron orbitals Electron configuration of Zr and Zr 4+ §[Kr]4d 2 5s 2 and [Kr] For Fe, Fe 2+, and Fe 3+ §[Ar]4s 2 3d 6, [Ar]4s 2 3d 4, [Ar]4s 2 3d 3 Effective nuclear charge  Z eff =Z-  àRelated to electron penetration towards nucleus

3-26 Atomic Radii Increase down a group Decrease across a period §Lanthanide and actinide contraction for ionic radius

3-27

3-28 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

3-29 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?

3-30 Pop Quiz Discuss the reaction necessary for the formation of 12 C in stellar processes. Why is this unusual?