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Understanding Stable vs. Unstable Nuclei in Nuclear Chemistry

Chapter 21 explores the differences between stable and unstable nuclei. Most nuclei are stable, while some are unstable (radioactive) and can spontaneously change into different nuclei, releasing radiation. Key topics include the types and uses of nuclear radiation, decay processes like alpha, beta, and gamma decay, and the concept of half-life, particularly in relation to carbon-14 dating. It also discusses the belt of stability, transmutation, and practical applications of nuclear reactions in medicine and technology.

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Understanding Stable vs. Unstable Nuclei in Nuclear Chemistry

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  1. Nuclear Chemistry Chapter 21

  2. Stable vs. Unstable Nuclei • Most nuclei are stable – do not change • Some nuclei are unstable (radioactive) • Change into a different nucleus • Spontaneous process – happens naturally, by itself • Releases radiation Only nuclear reactions can change a nucleus. No chemical process can

  3. Radium  Radon + Radiation • The radium was unstable (radioactive) • Turned into a different element (decayed) • The lost mass was turned into radiation

  4. Nuclear Radiation • Is spontaneously emitted from a radioactive nucleus • Can not be seen, smelled, heard • Can be detected using a Geiger counter or photographic film

  5. Uses of Radiation • Nuclear fuel (235U and 239Pu) • Nuclear Weapons • Irradiated Food • Smoke Alarms (Amercium-241) • Cancer treatment (Cobalt-60) • Medical Tracers

  6. Types of Nuclear Radiation 2 p+ 2 n e-

  7. The Electromagnetic Spectrum Light Dangerous (ionizing) Safe radiation (non-ionizing) Produced by nuclear decay

  8. What Stops Radiation Al Foil Wood Lead. Iron, Concrete Paper Alpha (a) Beta (b) Gamma (g)

  9. Decay Equations Alpha Decay 23892U  42He + 23490Th Beta Decay 23490Th 0-1e + 23491Pa

  10. Decay Equations Gamma Decay Occurs with alpha and beta decay No change in atomic mass (gamma radiation has no mass 00g)

  11. Decay: Ex 1 What product is formed when radium-226 undergoes alpha decay? 22688U  42He + ? 22688U  42He + 22286Rn

  12. Decay: Ex 2 What element undergoes alpha decay to form lead-208? ?  42He + 20882Pb 21284Po  42He + 20882Pb

  13. Decay: Ex 3 What isotope is produced when thorium-231 beta decays? 23190Th  0-1e + ? 23190Th  0-1e + 23191Pa

  14. Positron Emission • Same mass an electron, but opposite charge • Form of anti-matter 01e Electron Capture • Nucleus captures a core electron • electron is added rather than lost

  15. Common Particles

  16. Decay: Ex 4 Write the equation that describes oxygen-15 undergoing positron emission. Write the equation that describes mercury-201 undergoing electron capture

  17. Which nuclei are radioactive (unstable) • All elements have at least one radioactive isotope • All isotopes of elements heavier than Lead (element 82) are radioactive • All elements heavier than 92 (U) are man-made and radioactive 82 Pb 207.2 At least one radioactive isotope All isotopes are radioactive

  18. Belt of stability – based on neutron:proton ratio • Below ~20 = 1:1 ratio stable • Ratio increases with increasing # protons • Isotopes outside the belt try to decay and get on the belt

  19. Decay Modes • Above belt • Too many neutrons • Beta emission • Below belt • Too few neutrons • electron capture or positron emission • Atomic # >84 • Alpha Decay

  20. Most heavy isotopes (above 84) decay by alpha emission • Slide down to lead-206

  21. Decay Modes: Ex 1 Predict the decay mode for carbon-14 8n : 6p Too many n’s, prefers 1:1 146C  0-1e + 147N (ratio now 1:1)

  22. Decay Modes: Ex 2 Predict the decay mode for xenon-118 64n : 54p =1.2 Too few n’s (check graph) 11854Xe +0-1e  11853I or 11854Xe  0-1e + 11853I

  23. Decay Modes: Ex 3 Predict the decay mode for plutonium-239 Predict the decay mode for indium-120

  24. Further Observations • Magic #’s - Nuclei with 2, 8, 20, 28, 50 or 82 protons or 2, 8, 20, 28, 50 or 126 neutrons are especially stable. • Nuclei with even #s of both protons and neutrons are more stable than those with odds numbers. Ex: 63Cu and 65Cu are abundant, but 64Cu is not. Why?

  25. Transmutation • Rutherford(1919) – First successful alchemist 147N + 42He  178O + 11H 147N(a,p) 178O • Modern methods • Particle Accelerators (Cyclotrons) • Use neutrons or other elements (creation of transuranium elements)

  26. Transmutation: Ex 1 Write the balanced nuclear equations for the process : 2713Al(n, a) 2411Na

  27. Transmutation: Ex 2 Write the shorthard notation for: 168O + 11H  137N + 42He

  28. Transmutation: Neutrons • Neutrons produced from radioactive decay • Cobalt-60 is used in radiation therapy 5826Fe + 10n  5926Fe 5926Fe  5927Co + 0-1e 5927Co + 10n  6027Co

  29. Transmutation: Transuranium Elements 23892U + 10n  23992U  23993Np + 0-1e 23094Pu + 42He  24296Cm + 10n 20983Bi + 6428Ni  272111Uuu + 10n

  30. Half-Life • Half-life - The time during which one-half of a radioactive sample decays • Ranges from fraction of a second to billions of years. • You can’t hurry half-life.

  31. Carbon-14 dating • 14C atoms get incorporated into living things through breathing and eating. • Ratio of 14C to12C in a living organism is equal to that in the atmosphere • When an organism dies, the ratio changes as 14C radioactively decays. The amount of 14C starts to decrease over time.

  32. Carbon-14 dating • By measuring the amount of 14C in traces of once-living organisms, one can determine how long ago it died. • E.g., a 5730 years after death, only half of the 14C remains. • Reasonable to up to 50,000 years. • There is a 15% margin of error • Used in mummies, the Dead Sea Scrolls, Shroud of Turin

  33. Half-Life The polonium-214 will decay much sooner than the uranium. The uranium will be radioactive pretty much until the earth is destroyed when our sun goes out in 10 billion years.

  34. Half-life: Example 1 Carbon-14 has a half-life of 5730 years and is used to date artifacts. How much of a 26 g sample will exist after 3 half-lives? How long is that?

  35. Half-life: Example 1

  36. Half-life: Example 2 Tritium undergoes beta decay and has a half life of 12.33 years. How much of a 3.0 g sample of tritium remains after 2 half-lives?

  37. Solution to Problem

  38. Half-life: Example 3 Radon-226 has a half-life of 1600 years? How much of a 30 gram sample remains after 6400 years?

  39. Solution to Problem

  40. Half-life: Example 4 Cesium-137 has a half-life of 30 years. If you start with a 200 gram sample, and you now have 25 grams left, how much time has passed?

  41. Solution to Problem

  42. Half-life: Example 5 Calcium-45 has a half-life of 160 days. If you start with a 500 gram sample, and you now have 31.25 grams left, how much time has passed?

  43. Solution to Problem

  44. Rate Law First order rate law Rate = kN (N is the initial concentration) Rate = -DN = dN = -kN Dt dt dN = -kN dt dN = -kdt N

  45. ∫dN = ∫-kdt N ∫dN = -k∫dt (Integrate left from N0 to Nt N and time from 0 to t) lnNt = -kt N0

  46. Calculating k or the half-life lnNt = -kt N0 ln1 = -kt½ 2 k = 0.693 t½

  47. Rate Law: Ex 1 Uranium-238 has a half-life of 4.5 X 109 yr. If 1.000 mg of a 1.257 mg sample of uranium-238 remains, how old is the sample? k = 0.693 t½ k = 0.693 = 1.5 x10-10 yr 4.5 X 109 yr

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