Radioactivity

1. Radioactivity Spontaneous emission of small particles and/or radiation (energy) by unstable atomic nuclei to attain more stable nuclear state

3. Nuclide: nucleus with specified number of protons and neutrons Symbolized as AzX X - symbol of element A - mass number = nuclear mass Z - atomic number = nuclear charge Isotope: nuclides with same atomic # but different mass #s

4. Radionuclide: Radioactive nuclide (unstable nucleus) Radioactive isotope (radioisotope): isotope w/radioactive nuclide Radioactive decay: process of all radioactive decay until isotope with stable nucleus is reached Transmutation: nucleus reacts with another nucleus, elementary particle, or photon (gamma particle) to produce one or more new nuclei Nuclear equation: representation of change that occurs within or among atomic nuclei

5. Balancing rules for nuclear equations • Sum of mass #s of reactants must equal sum of mass #s of products (conservation of mass number) • 14 + 4=18=17 + 1 • Sum of nuclear charges of reactants must equal sum of nuclear charges of products (conservation of atomic number) • 7 + 2 = 9 = 8 + 1

8. Nuclear Stability • Hg: atomic mass = 200 • atomic # = 80 • #P = 80, #N = 120 • N/P ratio is 120/80 = 1.50 • Neutron-to-proton ratio • Low atomic numbers • Ratio close to 1 • Fall in zone of stability • Atomic # increases (21-83) • Z > 20, #N always exceeds #P protons in stable isotopes • Ratio gradually increases from 1 to 1.5 • > 83 (Bismuth) no stable nuclides • All radioactive and their isotopes decay • Lie outside zone of stability

9. alpha emission beta emission positron emission and electron capture

10. What is emitted depends upon location by zone of stability • Left of zone (mass # > atomic wt) • Neutron rich (tries to gain protons/lose neutrons) – NP + beta particle • Decays by β emission • Right of zone (mass # < atomic wt) • Proton rich (tries to lose protons/gain neutrons) – PN + positron • Decays by positron emission/electron capture • On zone, but Z>83 • Often decay by emitting alpha particles (usually above 60)

11. 24196Cf undergoes electron capture • 24196Cf + 0-1e  24195Am • 24195Am produces an αparticle • 24195Am  24193Np + 42He • 12154Xe produces a βparticle • 12154Xe  12153I + 01e • 16467Ho + 0-1e  ? • 16467Ho + 0-1e  16466Dy • 15867?  15866Dy + 01e • 15867Ho  15866Dy + 01e • 24294Pu  23892U + ? • 24294Pu  23892U + 42He

12. Magic Numbers Isotopes w/even # nucleons (P + N) tend to be more stable than those w/odd # nucleons Nuclei w/certain specific # P/N within nucleus ensure extra degree of stability Nucleus much less likely to absorb additional neutron Magic numbers for P/N are 2/8/20/28/50/82/126 Correspond to filling of shells in structure of nucleus When nuclei has P/N both in magic numbers, very stable and in high abundance in universe 3015P < 3920Ca < 4020Ca P-30-least stable-odd #s of both P/N C-39-even #P (20)/odd #N-even #P and "magic number"-more stable than P-30 Ca-40-most stable-even #P/N-both #s "magic numbers"

13. 11 11 2 1133 1146 4 11 51010 5 11 6 1520 15 6 11 7 21 3535217 11 8 28 56 7056288 11 9 36 84 126 12684 36 9 1 Pascal`s Triangle

14. Odd-even rule When #N/P both even numbers, isotopes tends to be far more stable than when they are both odd Of all 264 stable isotopes, number of protons/neutrons 168-even/even 57-even/odd 50-odd/even 4-odd/odd

15. Radioactive series (nuclear disintegration series) • Some nuclei cannot gain stability w/single emission

16. 24797Bk undergoes decay to what element after ααβααβαβααααββα?

17. Nuclear Transmutations • Nuclear reactions induced by nucleus gaining neutron or another nucleus • Converts nucleus into another nucleus • Can be represented by listing, in order, target nucleus, bombarding particle, ejected particle, and product nucleus

18. Homework: Read 18.1, pp. 877-882 Q pp. 906-907, #9a, 10, 12, 14, 16, 18

19. Rates of decay • Unstable atomic nucleus loses energy by emitting radiation • Spontaneous • Without collision w/another particle • Radioactive decay rates obey first-order kinetics • Instantaneous rate of decay of N radioactive atoms is directly proportional to # atoms present at that instant in time • Unit of activity • Becquerel (bq) – SI unit • 1 Bq is one transformation (decay) per second • Curie (Ci) • Originally based on activity of 1 g radium (1 Ci = 3.7 x 1010 Bq)

20. Radioactivity of substance may be measured decay rate • Decay rate = # atoms disintegrating per unit time = λN • λ (k) = first-order rate constant (decay constant) • N = # atoms of particular radioisotope present in sample • X = concentration of reactant at any moment • Xo = initial concentration • Integrated first-order equation • N = # atoms of radioisotope present in sample after time t has elapsed • N0 = # atoms of radioisotope present initially

21. Rate constant for 14C is much larger than rate constant for 238U • 14C: k = 1.210 x 10-4 yr-1 • 238U: k = 1.54 x 10-10 yr-1 • Therefore, 14C decays much faster than 238U • Half life for decay of 14C is much shorter than that of 238U • 14C: t1/2 = 5730 yr • 238U: t1/2 = 4.51 x 109 yr • Therefore, 14C decays much faster than 238U

22. http://www2.wwnorton.com/college/chemistry/gilbert/tutorials/interface.swf?chapter=chapter_02&folder=half_lifehttp://www2.wwnorton.com/college/chemistry/gilbert/tutorials/interface.swf?chapter=chapter_02&folder=half_life Half-life • Time it takes for exactly half of nuclei of radioactive sample to decay (activity of source of radiation to fall to half its starting level) • Time it takes for # atoms in sample to halve • Integrated form of first-order rate law in which N is substituted for concentration of X

23. Generic Half-Life Chart

24. The half-life of 23994Pu is 2.411 x 104 years. How many years will elapse before 99.9% of a given sample decomposes? • We have no specific amounts. However, we do know that 0.999 of our original 1.000 decomposes, leaving 0.001 remaining. We can thus establish the ratio N/N0 as 0.001/1.000. We can find k from t1/2. • k = 0.693/ t1/2 = 0.693/ 2.411 x 104 yr = 2.87 x 10-5/yr • ln [N/N0] = -kt = ln(0.001) = 2.87 x 10-5/yr • t = 2.87 x 105 yr • Total time is about 10 half-lives. We should have about 1/210 (or 0.001) of our original material remaining, and we do.

25. The half-life of protactinium-217 is 4.9 x 10-3 s. How much of a 3.50 mg sample of 21791Pa will remain after 1.000 sec? # half-lives = 1 half-life x 1.000s = 204 4.9 x 10-3 s • ½204 = 3.9 x 10-62 • 3.50 (3.9 x 10-62) = 1.4 x 10-61 mg • Because of the short half-live, essentially none of original nuclide remains after one second.

26. Homework: Read 18.2-18.3, pp. 883-889 Q pp. 907-908, #19, 20, 23, 26, 28

27. Aging carbon-containing materials • 14C is not natural isotope • Constantly formed in upper atmosphere • 14N is bombarded w/neutrons, keeping proportion of 14C relatively constant • When alive, plants/animals maintain same proportion of 14C in bodies because C continuously recycled • When organism dies • 14C no longer replenished by diet • Fraction of isotope in dead organic matter decreases with time • By comparing living/ancient 14C and comparing them • Reliably determine ages of biological materials that range from 1700 to 17,000 years old (half-life of C-14 is 5730 years) • Rule of thumb for radioactive isotope dating of materials • Age of sample should be 0.3 - 3 half-lives of isotope used for dating

29. A sample of bone taken from an archeological dig was determined by radiocarbon dating to be 12,000 years old. If we assume that a constant atmospheric C-14/C-12 ratio has 13.6 disintegrations per minute per gram of carbon, how many disintegrations per minute per gram does our 12,000 year old sample give off (half-life for carbon-14 = 5730 year)? • k = 0.693/t1/2 = 0.693/5730 yr = 1.21 x 10-4/yr. • ln(N/N0) = -kt = (- 1.21 x 10-4/yr)(12,000 yr) = -1.45 • N/N0 = e-1.45 = 0.234 • N0 = 13.6 disintegrations, so N = 0.234(13.6) • N = 3.2 disintegrations per minute per gram

30. If we start w/1.000 g of strontium-90, 0.953 g will remain after 2.00 yr. • What is the half-life of strontium-90? • k = -1/t ln Nt/NO • = -1/2.00 yr ln 0.953g/1.000g • k = -1/2.00 yr (-0.0481) = 0.0241 yr-1 • T1/2 = 0.693/k = 0.693/0.0241 yr-1 = 28.8 yr • How much strontium-90 will remain after 5.00 yr? • ln Nt/NO = -kt = (0.0241 yr-1)(5.00 yr) = -0.120 • Nt/NO = e-0.120 = 0.887 g (ev or INV LN function of calculator) • Nt = (0.887)NO = (0.887)(1g) = 0.887 g • What is the initial activity of the sample in Bq and in Ci? • k = (0.0241/yr)(1 yr/365 days)(1 day/24 hr)(1 hr/3600 s) = 7.64 x 10-10 s-1 • (1.000 g Sr-90)(1 mol Sr-90/90 g Sr-90)(6.022 x 1023 atoms Sr/1 mole Sr-90) = 6.7 x 1021 atoms • Total disintegrations/s = (7.64 x 10-10 disintegrations/atom - s)(6.7 x 1021 atoms ) = 5.1 x 1012 disintegrations/s = same as Bq • (5.1 x 1012 disintegrations/s)(1 Ci/ = 3.7 x 1010 disintegrations/s) = 1.4 x 102 Ci

31. Most devices for detecting radioactivity depend on formation of ions • Darkening of photographic plates, discharging of electroscopes, and damage to biological tissue all involve ionization • Geiger counter (Geiger-Müller tube) • Particle-produced ions trigger electricity pulse that is counted • Beta/gamma radiation • Cloud chambers • Measure charged particles (including alpha/beta particles) • Scintillation counters • Measure many different types • Flashes produced counted as measure of # particles emitted • Film dosimeters • Film reveals whether worker exposed to excess radiation • Gives total dose of radiation received

32. Nuclear energy • One important consequences of Einstein's theory of relativity was discovery of equivalence of mass and energy • Total energy content (E) of system of mass, m is given by Einstein's theory • E = mc2 where c is velocity of light (3.0 x 108 m/s) • Nuclear energies expressed in electronvolt (eV) and megaelectronvolt (MeV = 106eV) • 1 eV = 1.602 x 10-19 J; 1 MeV = 1.602 x 10-13 J • 1 u (atomic mass unit of mass) = 1.661 x 10-27 kg = 931.5 MeV of energy

33. Mass of nucleus is direct measure of its energy content Atomic mass of He is 4.002603 u  Add up mass of P/N/E There is difference of 0.030377 u All atoms are lighter than sum of masses of protons (1.007825 g), electrons, and neutrons (1.008665 g) Mass defect, Δm, equal to total mass of products minus total mass of reactants (difference between total mass of nucleons and measured mass of nucleus itself) Reflects stability of nucleus

34. To extract proton/neutron from nucleus, we have to pull pretty hard  Find that it will regain missing mass Binding energy defined as energy released when nucleus is assembled from its constituent nucleons Equal to energy needed to tear nucleus apart into its nucleons (so mass defect same as binding energy) Literally energy that binds together N/P in nucleus So with our helium atom, missing 0.030377 u released when nucleons come together That energy has to be put back to split nucleus up again

35. Binding energy measures difference between stability of products of reaction and starting materials • Provides quantitative measure of nuclear stability • Larger the binding energy (more negative), more stable nucleus is toward decomposition • Average binding energy per nucleon-binding energy of nucleus divided by mass number • Larger binding energy per nucleon, more stable nucleus is

36. Calculate the mass change for decay of mole of U-238. • 23892U  23490Th + 42He • 233.9942 g + 4.0015 g – 238.0003 g = -0.0046 g • ΔE = Δ(mc2) = c2Δm • (3.00 x 108 m/s) 2(-0.0046 g)(1kd/1000g) • -4.1 x 1011 kg-m2/s2 = -4.1 x 1011 J • Notice Δm converted to kg (SI unit of mass) to obtain ΔE in joules (SI unit for energy) • Negative sign indicates energy is released in reaction (over 400 billion joules/mole of U)

37. Determine the binding energy in J/mol and MeV/nucleon for 10146Pd (atomic mass = 100.908287 g/mol). • Mass of individual nucleons 46 x 1.007825 g/proton = 46.35995 g 55 x 1.009665 g/neutron = 55.476575 g 101.836525 g/mol • mass defect = 101.836525 g – 100.908287 g = 0.928238 g • ∆E = ∆mc2 = -9.28238 x 10-4 kg (3.00 x 108 m/s)2 (minus sign because mass is lost in forming the nuclide) ∆E = -8.35 x 1013 J/mol -8.35 x 1013 J 1 MeV 1 mol 1 nuclide = -8.59 MeV mol 1.60 x 10-13 J 6.02 x 1023 nuclides 101 nucleons nucleon

38. Natural Radioactivity • Few naturally occurring radioactive isotopes • K-40 decays into Ar-40, found in air • C-14 determines age of artifacts • Vanadium-50, Tritium (H-3), radon, thorium, lanthanuim-138 • Polonium, Z=84 to uranium, Z=92 • Radon-222 forms from decomposition of U in rocks (granite) • Gathers in lower, unventilated areas of houses • Gas decomposes into solid polonium, which if decays in lungs, emits alpha particles which can cause cancer • Radium-226-causes biological damage • U-238 used to determine age of very old rocks as it decays to lead-206 • Transuranium elements (93-118) artificially prepared/radioactive

39. Used depending on properties of particular isotope Tracers to uncover how certain chemical reactions occur Phosphorus-32 shows details of how plants use P to grow/reproduce Medical applications (radioactivity/short half-life necessary to ensure rapid decay and elimination from body) Diagnostics (PET scan) Treatment (I-131 for thyroid cancer) Determine age of various artifacts (C-14) Smoke detectors (Americium-241) Food irradiation (gamma rays) Irradiation in pest control

40. Artificial Radioactivity • Artificial radioactivity results when unstable nucleus produced by transmutation • Nuclear transmutation-process of converting one element into another • Al atoms bombarded w/alpha particles produces radioactive P-30 • P-30 decays by positron emission and has half-life of 2.5 min • Does not occur naturally in phosphorus compounds

41. Induced transmutation Neutrons easily captured by stable nuclei No charge Not repelled by target nuclei No KE needed to overcome electrostatic repulsion if protons/alpha particles used Readily produce "artificial" radioactivity New nucleus formed has higher n : p ratio Leads to product that decays by beta decay Neutron capture by chlorine-37 yields chlorine-38

42. Nuclear transmutation processes are abbreviated using Target nucleus (bombarding particle, ejected particle) Product nucleus n, p, d, α, e, and γ used to represent neutron, proton, deuteron, alpha particle, electron, and gamma ray

43. Nuclear Fission-any process that yields two nuclei of almost equivalent mass • Does not occur spontaneously • Requires bombardment of fissile nucleus (23592U or 23994Pu) • By energetic neutrons • That causes release of several more neutrons • Chain reaction • Neutrons released in each fission start additional fissions • Two ways to keep fission from becoming uncontrolled • Small enough sample so released neutrons will not hit other U-235 nuclei to continue chain reaction • Critical mass of several pounds needed before chain reaction will be sustained (explosion) • Excess neutrons can be absorbed by certain materials (graphite, paraffin) • Control rods adjust number of available neutrons and rate of nuclear reactions

44. Fission reactors-employs controlled chain reaction to provide continuous source of useful energy Containment shell of concrete/steel for shielding Fuel rods in core as source of energy (enriched U-235) Moderator creates neutrons for reaction Control rods regulate rate of fission (cadmium) Coolant (water/liquid Na) removes thermal energy from core Heat exchanger receives thermal energy and produces steam for generation of electrical energy by turbine connected to reactor Problems Heat causes thermal pollution Radioactive waste disposal Benefits Energy Produce radioactive isotopes

45. Nuclear Fusion-combination of two nuclei to form a larger, more stable nucleus • For self-sustaining fusion reaction to occur • Temperatures of 40,000,000 K needed • Nucleus has higher average binding energy per nucleon • Because all nuclei positively charged, they must collide with enormous force to combine • At these temperatures, gases completely ionized into mixture of positive nuclei and electrons (plasma) • One gram of hydrogen upon fusion releases energy equivalent to combustion of 20 tons of coal • Fusion of four moles of H atoms releases 2.6 x 109 kJ of energy + 2γ + 2ν (neutrino)

46. Interaction of radiation with matter • Alpha/beta/gamma rays pass through matter • Alpha/beta particles colliding with electrons • Lose small fraction of their energy in collision • Forcefully eject electrons from atoms/ molecules • Because alpha/beta particles extremely energetic, thousands of collisions required to bring them to rest • Produce ions • Particles produce "tracks" of ionization • Alpha/beta/gamma rays known as ionizing radiation

47. Units of Radiation Dose-rad and rem • Rad (radiation absorbed dose) • 0.01 joule of energy absorbed per kilogram • Beams of different radiations cause very different biological damage even when body absorbs same amount of energy from each type, it is necessary to define unit specifically for biological tissue • rem (radiation equivalent in man) • Absorbed dose in rads x relative biological effectiveness factor, RBE • dose (in rem) = RBE x dose (in rad) • For beta and gamma rays RBE = 1.0; for fast neutrons and alpha particles RBE = 10 • Dose of one rad of alpha radiation = 10 rem

48. Homework: Read 18.4-18.7, pp. 889-903 Q pp. 908-909, #33, 34, 38, 44 Do 1 additional exercise and 1 challenge problem Submit the quizzes by email to me: http://www.cengage.com/chemistry/book_content/0547125321_zumdahl/ace/launch_ace.html?folder_path=/chemistry/book_content/0547125321_zumdahl/ace&layer=act&src=ch18_ace1.xml http://www.cengage.com/chemistry/book_content/0547125321_zumdahl/ace/launch_ace.html?folder_path=/chemistry/book_content/0547125321_zumdahl/ace&layer=act&src=ch18_ace2.xml http://www.cengage.com/chemistry/book_content/0547125321_zumdahl/ace/launch_ace.html?folder_path=/chemistry/book_content/0547125321_zumdahl/ace&layer=act&src=ch18_ace3.xml