Chapter 21: Nuclear Chemistry

1. Chapter 21: Nuclear Chemistry Chemistry: The Molecular Nature of Matter, 6E Jespersen/Brady/Hyslop

2. + + How are atoms formed? • Big Bang—Intense heat ~109 K • Cooled quickly to 106 K—T of stars • e–, p, n formed and joined into nuclei—atoms • Mostly H and He (as in our sun) • Rest of elements formed by nuclear reactions • Fusion—two nuclei come together to form another heavier nucleus • Fission—one heavier nucleus splits into lighter nuclei • Various other types of reactions

3. Nuclear Shorthand • Nucleons • Subatomic particles found in the nucleus • Protons (p) • Neutrons (n) • Nuclide • Specific nucleus with given atomic number (Z) • Atomic Number (Z) • Number of protons in nucleus • Determines chemical properties of nuclide • Z = p • Mass Number (A)—mass of nuclide • A = n + p

4. Shorthand for Writing Nuclides • Where X = atomic symbol • e.g. • In the neutral atom: e– = p = Z • Isotopes • Nuclides with same Z (same number of p), but different A (different n)

5. Radioactivity • Radioactive isotopes • Isotopes with unstable atomic nuclei • Emit high energy streams of particles or electromagnetic radiation • Radionuclides • Another name for radioactive isotopes • Undergo nuclear reactions • Uses • Dating of rocks and ancient artifacts • Diagnosis and treatment of disease • Source of energy

6. Mass Not Always Constant • Mass of particle not constant under all circumstances • It depends on velocity of particle relative to observer • As approaches speed of light, mass increases • When v goes to zero • Particle has no velocity relative to observer • v/c 0 • Denominator  1 • and m = mo m = mass of particle v = velocity of particle m = rest mass c = speed of light

7. Why don’t we observe mass change? • In lab and ordinary life, velocity of particle is small • Only see mass vary with speed as velocity approaches speed of light, c • As v c, (v/c)  0 and m  ∞ • In lab, m = mo within experimental error • Difference in mass too small to measure directly • Scientists began to see relationship between mass and total energy • Analogous to potential and kinetic energies

8. Law of Conservation of Mass and Energy • Mass and energy can neither be created nor destroyed, but can be converted from one to the other. • Sum of all energy in universe and all mass (expressed in energy equivalents) in universe is constant • Einstein Equation • E = (mo)c2 • Wherec = 2.9979 × 108 m/s

9. Mass Defect • Rest mass of nuclide is always less than sum of masses of all individual nucleons (neutrons and protons) in that same nuclide • Mass is lost upon binding of neutrons and protons into nucleus • When nucleons come together, loss of mass translates into release of enormous amount of energy by Einstein's relation Energy released = – Nuclear Binding Energy • Nuclear Binding Energy • Amount of energy must put in to break apart nucleus

10. What is Mass Loss? For given isotope of given Z and A or

11. Ex.1 Binding Energy Calculation What is the binding energy of 7Li3+ nucleus? Step 1. Determine mass loss or mass defect A. Determine mass of nucleus mass of 7Li3+ = m(7Li isotope) – 3me = 7.016003 u – 3(0.0005485 u) = 7.0143573 u B. Determine mass of nucleons mass of nucleons = 3 mp + 4 mn = 3(1.007276470 u) + 4(1.008664904 u) =7.056489026 u

12. Ex. 1 Binding Energy Calculation (cont.) C. m = mnucleus – mnucleons = 7.0143573 u – 7.056489026u = –0.0421317 u = mass lost by nucleons when they form nucleus Step 2. Determine energy liberated by this change in mass E = (mo)c2 E = – 6.287817 × 10–12 J/atom

13. Ex. 1 Binding Energy Calculation (cont.) E = –6.287817 × 1012 J/atom × 6.0221367 x 1023 atoms/mole E = –3.78655 × 1012 J/mole = –3.78655 × 109 kJ/mole Compare this to: • 104 – 105 J/mol (102 – 103 kJ/mol) for chemical reactions • Nuclear ~ 1 – 10 million times larger than chemical reactions!!

14. MeV (Energy Unit) • Nuclear scientists find it convenient to use a different Energy unit: MeV (per atom) • Electron volt (eV) • Energy required to move e across energy potential of 1 V • 1 eV = 1.602 × 10–19 J • M(mega) = 1 × 106 • So 1 MeV = 1 × 106 eV • 1 MeV = 1.602 × 10–13 J

15. Ex. 1 Binding Energy Calculation in MeV • For Ex. 1. Converting Eto MeV gives • Often wish to express binding energy per nucleon so we can compare to other nuclei • For Li3+ with 3 1p and 4 n this would be

16. Ex. 2 Calculate E Released • The overall reaction in the sun responsible for the energy it radiates is • How much energy is released by this reaction in kJ/mole of He? m (1H) = 1.00782 u m (4He) = 4.00260 u m (0+) = 0.00054858 u

17. Ex. 2 Calculate E Released (cont.) • m = mproducts – mreactants • m = m(4He) +2m(e+) – 4m(1H) • m = 4.00260 u + 2(0.00054858 u)– 4(1.00782 u) • m = –0.02758 u • [We will convert u to kg, kg m2/s2 to J, and atoms to moles in the following calculation] E = –2.479 × 1012 J/mol = –8.268 × 109 kJ/mol

18. Your Turn! Determine the binding energy, in kJ/mol and MeV/atom, for an isotope that has a mass defect of –0.025861 u. A. –2.3243 × 109 kJ/mol; 24.092 MeV/atom B. –3.8595 × 10–12 kJ/mol; 24.092 MeV/atom C. –7.7529 kJ/mol; 8.03620 × 10–8 MeV/atom D. –2.3243 × 109 kJ/mol; 4.1508 × 10–2 MeV/atom

19. Your Turn! - Solution

20. Binding Energies per Nucleon • Divide binding energy EB by mass number, EB/A • Get binding energy per nucleon

21. Implications of Curve • Most EB /A in range of 6 – 9 MeV (per nucleon) • Large binding energy EB /A means stable nucleus • Maximum at A = 56 • 56Fe largest known EB /A • Most thermodynamically stable • Nuclear mass number (A) and overall charge are conserved in nuclear reactions • Lighter elements undergo fusion to form more stable nuclei

22. Implications of Curve Fusion • Researchers are currently working to get fusion to occur in lab • Heavier elements undergo fission to form more stable elements Fission • Reactions currently used in bombs and power plants (238U and 239Pu) • As stars burn out, they form elements in center of periodic table around 56Fe

23. Radioactivity • Spontaneous emission of high energy particles from unstable nuclei • Spontaneous emission of fundamental particle or light • Nuclei falls apart without any external stimuli • Discovered by Becquerel (1896) • Extensively studied by Marie Curie and her husband Pierre (1898  early 1920's) • Initially worked with Becquerel

24. Fun Facts • Marie and Pierre Curie discovered polonium and radium • Nobel Prize in Physics 1903 • For discovery of Radioactivity • Becquerel, Marie and Pierre Curie—all three shared • Nobel Prize in Chemistry 1911 • For discovery of Radium and its properties • Marie Curie only • Marie Curie - first person to receive two Nobel Prizes and in different fields

25. Discovery of Radioactivity • Initially able to observe three types of decay • Labeled them , ,  rays (after first three letters of Greek alphabet) • If they pass through an electric field, very different behavior

26. Discovery of Radioactivity •  rays attracted to negative pole so its positively charged •  rays attracted to positive pole so its negatively charged •  rays not attracted to eitherso its not charged   

27. Nuclear Equations • Used to symbolize decay of nucleus e.g. 238U234Th + parentdaughter • Produce new nuclei so need separate rules to balance Balancing Nuclear Equations • Sum of mass numbers (A, top) must be same on each side of arrow • Sum of atomic numbers (Z, bottom) must be same on each side of arrow 92 90

28. Types of Spontaneous Emission • Alpha()Emission He nucleus 2 n + 2 p A = 4 and Z = 2 • Daughter nuclei has: Adecreases by 4 A = – 4 Zdecreases by 2 Z = – 2 • Very common mode of decay if Z > 83 (large radioactive nuclides) • Most massive particle • e.g.

29. Balancing Nuclear Equations • The sum of the mass numbers (A; the superscripts) on each side of the arrow must be the same • The sum of the atomic numbers (Z; the subscripts; nuclear charge) on each side of the arrow must be the same • e.g. A: 234 = 230 + 4 Z: 92 = 90 + 2

30. Emission of electrons Mass number A = 0 and charge Z = –1 But How? No electronsin nucleus! If nucleus neutron rich — nuclide is too heavy 2. Beta (– or e–) Emission

31. Charge conserved, but not mass mE Ejectede–has very high KE + emits Antineutrino variable energy particle Accounts for extra E generated e.g. 2. Beta (– or e–) Emission

32. 3. Gamma () Emission • Emission of high energy photons • Often accompanies  or  emission • Occurs when daughter nucleus of some process is left in excited state • Use * to denote excited state • Nuclei have energy levels analogous to those of e– in atoms • Spacing of nuclear E levels much larger •  light emitted as -rays e.g.

33. 4. Positron (+ or e+) Emission • Emission of e+ • Positive electron • Where does + come from? • If nucleus is neutron poor) • Nuclide too light • Balanced for charge, but NOT for mass

34. 4. Positron (+ or e+) Emission • Product side has much greater mass! • Reaction costs energy • Emission of neutrino • Variable energy particle • Equivalent of antineutrino but in realm of antimatter • e+ emission only occurs if daughternucleus is MUCH more stable than parent

35. 4. Positron (+or e+) Emission What happens to e+? • Collides with electron to give matter anti-matter annihilation and two high energy -ray photons mE • Annihilation radiation photons • Each with E = 511 keV • What is antimatter? • Particle that has counterpart amongordinary matter, but of opposite charge • High energy light, massless • Detect by characteristic peak in -ray spectrum

36. 5. Electron Capture (EC) • e– in 1s orbital • Lowest Energy e– • Small probability that e– is near nucleus • e– actually passes through nucleus occasionally • If it does: • Net effect same as e+ emission

37. Types of Spontaneous Emission 6. NeutronEmission = ( ) • Fairly rare • Occurs in neutron rich nuclides • Does not lead to isotope of different element 7. Proton Emission = ( ) • Very rare

38. Types of Spontaneous Emission 8. Spontaneous Fission • No stable nuclei with Z > 83 • Several of largest nuclei simply fall apart into smaller fragments • Not just one outcome, usually several different—see distribution

39. Summary—Common Processes 1. Alpha () Emission • Very common if Z > 83 2. Beta () Emissione– • Common for neutron-rich nuclides—below belt of stability 3. Positron (+) Emission e+ • Common for neutron-poornuclides—above belt of stability 4. Electron Capture (EC) • Occurs in neutron-poor nuclides, especially if Z > 40 5. Gamma () Emission • Occurs inmetastable nuclei (in nuclear excited state)

40. –2 –2 0 –4 yes +1 –1 –1 0 yes –1 +1 +1 0 yes –1 +1 +1 0 yes 0 0 0 0 no Learning Check • Complete the following table which refers to possible nuclear reactions of a nuclide:

41. Learning Check Balance each of the following equations

42. Your Turn! What is the missing species, , in the following nuclear reaction? A. B. C. D.

43. What Holds Nucleus Together? • Consider nucleus • Neutrons and protons in close proximity • Strong proton-proton repulsions • Neutrons spread protons apart • Neutron to proton ratio increases as Zincreases Strong Forces • Force of attraction between nucleons • Holds nuclei together • Overcomes electrostatic repulsions between protons • Binds protons and neutrons into nucleus

44. Table of Nuclides • Chart where Rows = different atomic number Columns = different number of neutrons • Symbol entered if element is known • Stable nuclei • Natural abundance entered below symbol • Shaded area • Trend of stable nuclei = Belt of Stability • Z ≈ number of neutrons (for elements 1 to 20) • Unstable nuclei • Give type(s) of radioactive decay (spontaneous) • Outer edges, most of atoms

45. Table of Nuclides Number of neutrons Atomic number (Z = number of protons)

46. Table of Nuclides • Shaded area = stable nuclei • Trend of stable nuclei = diagonal line = Belt of Stability • Z ≈ number of neutrons (for elements 1 to 20) • Note: only a small corner of table is shown. (The complete is in Handbook of Chemistry and Physics)

47. Belt of Stability 1.5n:1p  Stable nuclide, natural  Unstable nuclide, natural  Unstable nuclide, synthetic • Each isotope is a dot • Up to Z = 20 • Ratio n /Z = 1 • As Zincreases, n > Z and • By Z = 82, n/Z ~1.5 • n = number of neutrons • Z = number of protons 1.4n:1p Band of Stability n e– emitters 1.3n:1p 1.2n:1p 1n:1p 1.1n:1p e+ emitters 1n:1p Z = p

48. How To Predict if Nuclei are Stable 1) Atomic Mass = weighted average of masses of naturally occurring isotopes, i.e. most stable ones 2) Compare atomic mass of element to A (atomic mass number) of given isotope and see if it is more or less • Atomic Mass > A too light to be stable • Atomic Mass < A too heavy to be stable 190.2 Too light, neutron poor Too heavy, neutron rich 126.9 • Final note: • All nuclei with Z > 83 are radioactive

49. More Patterns of Stability • If we look at stable and unstable nuclei, other patterns emerge • 283 stable nuclides (out of several thousand known nuclides) • If we look at which have even and odd numbers of protons (Z) and neutrons (n); patterns emerge 2H, 6Li, 10B, 14N, 138La

50. More Patterns of Stability • Clearly NOT random: even must imply greater stability • Not too surprising • Same is true of electrons in molecules • Most molecules have an even number of electrons, as electrons pair up in orbitals • Odd electron molecules, radicals, are very unstable, i.e. very reactive!!