1. Nuclides1 Introduction to Nuclides the big bang The big bang theory www.uwaterloo.ca/~cchieh/cact/nuctek/universe.html Einstein-Wheeler: "Matter tells space how to curve, and space tells matter how to move." 1927 Lemaitre: The universe began with an explosion based on red shift. Hubble observed the red shift proportional to distance of stars from us. 1964 Penzias and Wilson discovered the cosmic microwave background (CMB) radiation, as due to remnants of big bang. Depending on the outcome of the observations, the big bang theories will be abandoned, revised or extended to accommodate additional observartions. What is in the universe? How did the universe begin? Where did materials come from? Can material and energy really inter-convert into each other?

2. Nuclides2

3. 3 The Big Bang View All energy (and matter) in the universe concentrates in a region smaller than a marble 12 billions years ago. It started to expand and cool to a billion K. Elementary particles roamed free in a sea of energy. Further expansion caused a drop in temperature and confined quarks in neutrons and protons. Galaxies began to form. Galaxy clusters

4. Nuclides4 Hubble’s Observation One method for gauging distance is to observe the apparent brightness of a galaxy. The red shift shows that the universe is constantly expanding

5. Nuclides5 Cosmologic Matters Radiation : massless or nearly massless, photons (light) and neutrinos. Baryonic matter (Nuclides): composed primarily of protons, neutrons and electrons; has essentially no pressure of cosmological importance. Dark matter : exotic non-baryonic matter that interacts only weakly with ordinary matter; This form of matter also has no cosmologically significant pressure. Dark energy : a bizarre form of matter, or perhaps a property of the vacuum itself; characterized by a large, negative pressure; a form of matter that can cause the expansion of the universe to accelerate

6. Nuclides6 What is the history of the universe?

7. Nuclides7 Nuclides composite particles of nucleons Protons and neutrons are bound together into nuclei. Atoms contain a complement of electrons. A nuclide is a type of atoms whose nuclei have a specific numbers of protons and neutrons. Nucleons (protons and neutrons) are convenient units to consider nuclear changes, although the standard model considers quarks as basic components. Like particles, nuclides are energy states, with amounts properties. Some basic principles are seen for stability of nuclide. A nuclide A E Z A- mass number Z- atomic number eg. 238 U 92

8. Nuclides8 Stable Nuclides Stable nuclides remain the same for an indefinite period. Some characteristics of stable nuclides: Atomic number Z  83, but no stable isotopes for Z = 43 and 61. There are 81 elements with 280 stable nuclides. Usually there are more neutrons than protons in the nuclei. Nuclides with magic number of protons or neutrons are very stable. Pairing of nucleons (spin coupling) contributes to nuclide stability. Is abundance of a nuclide related to its stability?

9. Nuclides9 Stable Nuclides number of neutrons and protons Find N / Z for 4 He 2 = 1 16 O 8 = 40 Ar 18 = 91 Zn 40 = 144 Nd 60 = 186 Re 75 = 209 Bi 83 = N = # of neutrons Z = # of protons

10. Nuclides10 Stable Nuclides N/Z of some light nuclides Z 14 Si Si Si 13 Al 12 Mg Mg Mg. 11 Na 10 Ne Ne Ne 9 F. 8 <- magic #... O O O 7 N N 6 C C.. 5 B B 4 Be.. 3 Li Li 2. He He.. 1 P D. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 -> N

11. Nuclides11 Stable Nuclides N/Z of nuclides 40 Zr........ +... XXX X X 39 Y X 38 Sr X XXX 37 Rb X X 36 Kr X X XX X 35 Br..... +.. X X 34 Se XXXX X X 33 As X 32 Ge X XXX X. 31 Ga X X 30 Zn... +. X XXX X. 29 Cu X X 28 Ni X XXX X.. 27 Co X 26 Fe X XXX.. 25 Mn + X 24 Cr X XXX.. 23 v XX 22 Ti XXXXX... 21 Sc X 20 Ca X X 2 2 3 4 5 01234567890123456789012345678901 N / A ratio increases as A increases More stable isotopes for even Z than odd Z More stable isotones for even N than odd N More stable isotopes and isotones for magic Z and N

12. Nuclides12 Stable Nuclides natural occurring heavy nuclides Natural Occurring Isotopes of Heavy Elements ( abundance ) 76Os184 (0.018), 186 (1.59), 187 (1.64), 188 (13.3), 189 (16.1), 190 (26.4), 192 (41.0) 77Ir191 (38.5), 193 (61.5) 78Pt190 (0.0127), 192 (0.78), 194 (32.9), 195 (33.8), 196 (25.2), 198 (7.19) 79Au197 (100) 80Hg196 (0.146), 198 (10.02), 199 (16.84), 200(23.13), 201(13.22), 202(29.8), 204(6.85) 81Tl203 (29.5), 205 (70.5) 82 Pb204 (1.4), 206 (25.1), 207 (21.7), 208 (52.3) 83Bi209 (100) 90Th232 (100% half life 1.4x10 10 y) 92U235 (0.720, half life 7.04x10 8 y), 238 (99.276, half life 4.5x10 9 y)

13. Nuclides13 Stable Nuclides pairing of nucleons Effect of Paring Nucleons ZN # of stable stable nuclides eveneven166 evenodd57 oddeven53 oddodd*4 total 280 *They are: 2 D 1, 6 Li 3, 10 B 5, & 14 N 7 Two protons or neutrons occupy a quantum state, due to their ½ spin. Pairing nucleons stabilises nuclides, leading to a large number of stable nuclides with even Z and N. No stable isotopes for Z = 43 or 61. No stable isotones with N = 19, 31, 35, 39, 61, 89 More stable isotopes for even Z than odd Z and for even N than odd N Elements with even Z are more abundant than those with odd Z of comparable mass.

14. Nuclides14 Stable Nuclides magic numbers of nucleons Magic numbers are 2, 8, 20, 28, 50, 82, and 126. Double-magic number nuclides: 4 He 2, 16 O 8, 40 Ca 20, 48 Ca 20, & 208 Pb 82. 4 He 2 as alpha particles, abundant in the universe, 16 O 8 abundant on Earth. Six stable isotopes of Ca 20, 5 stable isotopes of Ni 28, high for their masses. Large number of stable isotopes and isotones with Z & N = 50 and 82. The heavies stable nuclide 209 Bi 83 has 126 neutrons. O 8, Ca 20, Ni 28, Sn 50 and Pb 82 have relative high abundance.

15. Nuclides15 Stable Nuclides abundances of elements Even Z elements are more abundant than odd Z ones of comparable mass.

16. Nuclides16 Stable and Radioactive Nuclides mass and stability of nuclides Mass and energy are equivalent, E = m c 2. Relative mass is the key for stability of nuclides. Energy drives changes. If a system can lower its energy, it will. Unstable nuclides undergo decay or fission, releasing energy stabilises the system. Discuss the stability of carbon isotopes. Half life 9 C127. ms 10 C19.3 s 11 C20.3 m 12 Cstable 13 Cstable 14 C5730. y 15 C2.45 s 16 C 0.75 s

17. Nuclides17 Stable and Radioactive Nuclides binding energy The binding energy ( BE ) of a nuclide is the energy released when the atom is synthesized from the appropriate numbers of hydrogen atoms and neutrons. Z H + N n = A E Z + BE or Z m H + N m n = m E + BE where m H, m n, and m E are masses of H, n, and A E Z respectively. Eg BE = Z m H + N m n - m E BE ( 3 He) = (2*1.007825 + 1.008665 - 3.01603) 931.481 MeV = 7.72 MeV BE ( 4 He) = (2*1.007825 + 2*1.008665 - 4.00260) 931.481 MeV = 28.30 MeV

18. Nuclides18 Stable and Radioactive Nuclides average binding energy The binding energy and average binding energy of some nuclides Nuclide BE BE / A MeV MeV / nucleon 3 He 2 7.72 2.57 4 He 2 28.3 7.08 16 O 8 127.6 7.98 56 Fe 26 492.3 8.79 54 Fe 26 471.768.74 208 Pb 82 1636.44 7.87 238 U 92 1801.7 7.57 BE A A

19. Nuclides19 The Average Binding Energy Curve

20. Nuclides20 Stable and Radioactive Nuclides mass excess (ME) The difference between the mass of a nuclide and its mass number, A, is the mass excess ( ME ), ME = mass - A. Masses (amu) of some entities H 1.00782503 18 O 17.99916 2 D2.014102 54 Fe54.938296 3 H 3.016049 56 Fe55.934939 4 He4.002603 206 Pb205.975872 12 C12.000000 209 Bi208.9804 14 C14.003242 235 U235.043924 16 O15.994915 238 U238.055040 What are the ME s for the nuclides listed here? Which is the standard? Which have negative ME s?

21. Nuclides21 Stable and Radioactive Nuclides mass excess (ME) and average -BE Comparison of mass excess and average binding energy (amu) Nuclide Mass ME - BE average BE H1.0078250.00782500 n1.0086650.00866500 3 He3.016030.01603-0.002760.00828 4 He4.002600.00260-0.00760.0304 12 C12.0000000-0.008250.09894 16 O15.994915-0.005085-0.008570.1369 40 Ca39.96259-0.03741-0.009170.3669 54 Fe53.939612-0.060388-0.009380.5065 56 Fe55.934939-0.065061-0.009440.52851 208 Pb 82 207.976627-0.023373-0.008451.757 238 U 92 238.0507840.050784-0.008131.934

22. Nuclides22 Stable and Radioactive Nuclides fission and fusion energy and ME

23. Nuclides23 Stable and Radioactive Nuclides application of mass excess (ME) Like masses, the ME can be used to calculate energy of decay, because the same scale is used for both. eg: ME ’s of 40 Sc 21 and 40 Ca 20 are -20.527 and -34.847 MeV respectively. Estimate the energy of decay for 40 Sc 21  40 Ca 20 +  + or 40 Sc 21 + e –  40 Ca 20 solution: E decay = -20.527 - (-34.847) = 14.32 MeV E decay includes 1.02 MeV for the positron-electron pair for  + decay.

24. Nuclides24 Stable and Radioactive Nuclides ME of isobars In 49 Sn 50 Sb 51 Te 52 I -53 Xe 54 Cs 55 Ba 56 -0.0896 -0.0943 -0.0958 -0.0967 -0.0944 -0.0915 -0.0870 -0.0808 Mass excesses (amu) of isobars with mass number 123: Z ME

25. Nuclides25 Stable and Radioactive Nuclides BE of isobars Plots of BE an ME are very similar, and either one can be used to show the decay of isobars. Only 57 Fe 26 is stable for isobars of mass 57. Mass. BE.amu.amu Cr 24 56.9434 0.53031 Mn 25 56.9383 0.53462 Fe 26 56.9354 0.53667 Co 27 56.9363 0.53493 Ni 28 56.3980 0.53240

26. Nuclides26 Stable and Radioactive Nuclides problem types Evaluate the BE of a nuclide tell nuclide with zero BE evaluate ME of a nuclide tell nuclide with zero ME evaluate decay energy estimate decay mode predict the stable isobar(s) estimate max kinetic energy of beta or positrons in beta decay Mass and BE of mass 57 isobars.Mass.BE.amu.amu Cr 24 56.9434 0.53031 Mn 25 56.9383 0.53462 Fe 26 56.9354 0.53667 Co 27 56.9363 0.53493 Ni 28 56.3980 0.53240

27. Nuclides27 Stable and Radioactive Nuclides ME of isobars continue Pairing of nucleons plays a role for stability of isobars with even mass numbers. There are even-even and odd-odd type of nuclides in isobars of even mass numbers

28. Nuclides28 Stable and Radioactive Nuclides a semi-empirical equation for BE BE(A,Z) = 14.1A - 13A 2/3 - - + Ea Proportional to A Decrease due to surface tension Instability due to p Instability due to neutron to proton ratio Pairing of nucleon

29. Nuclides29 Nuclides summary The big bang Factors for stable nuclides mass and stability