Nuclear Chemistry Study Guide

Chapter 21: Nuclear Chemistry

21.1 What is Radioactivity?

• Radioactivity is the process by which unstable atomic nuclei lose energy by emitting radiation.
• Parent radionuclide: an unstable nuclide that emits radiation and transforms into a daughter nuclide.
• Daughter nuclide: the product of the decay of a parent radionuclide.
• Nuclide: refers to the nucleus of an isotope characterized by its number of protons and neutrons.

Types of Radioactive Decay

1. Alpha (α) Decay: Emission of an alpha particle (2 protons, 2 neutrons).
   • Occurs in large nuclei (Z > 83).
   • Example:
     $^{238}<em>{92}U \rightarrow {^{234}</em>{90}Th} + {^{4}_{2}He}$
2. Beta (β) Decay: A neutron is transformed into a proton and emits a beta particle (a high-speed electron) and an antineutrino.
   • Occurs in nuclei with too many neutrons.
   • Example:
     $^{14}<em>{6}C \rightarrow {^{14}</em>{7}N} + {^{-1}_{0}e}$
3. Gamma (γ) Emission: High-energy electromagnetic radiation emitted after alpha or beta decay, often from an excited nucleus transitioning to a lower energy state.
   • Example:
     $^{60}<em>{27}Co \rightarrow {^{60}</em>{27}Co^*} \rightarrow {^{60}<em>{27}Co} + {0}</em>{0}γ$
4. Positron Emission: A positron (anti-electron) is emitted, converting a proton into a neutron.
   • Examples:
     $^{11}<em>{6}C \rightarrow {^{11}</em>{5}B} + {^{+1}_{0}e}$
5. Electron Capture: An electron from the surrounding electron cloud is captured by the nucleus, converting a proton to a neutron.
   • Example:
     $^{54}<em>{24}Cr + {^{-1}</em>{0}e} \rightarrow {^{54}_{23}V}$

21.2 Patterns of Nuclear Stability

• Nuclear stability is influenced by the neutron-to-proton (n:p) ratio.
  • For nuclei with Z ≤ 20, stable nuclei typically have an n:p ratio close to 1:1.
  • As Z increases, more neutrons are needed for stability. Nuclear isotopes can be plotted on a belt of stability.
• Nuclei above the belt generally decay by beta emission; those below decay by positron emission or electron capture.
• No stable nuclei exist with Z > 83, leading to alpha decay in heavier elements.

21.3 Nuclear Transmutations

• Nuclear Transmutation: A nuclear reaction that changes one element into another by bombarding it with high-energy particles.
  • Example:
    $^{14}<em>{7}N + {^{4}</em>{2}He} \rightarrow {^{17}_{8}O}$
  • Synthetic isotopes used in medicine (like Cobalt-60) are made via nuclear transmutation.

21.4 Rates of Radioactive Decay

• The rate of decay is modeled using the half-life, defined as the time required for half of the atoms of a radioactive sample to decay.
• The decay obeys a first-order process.
• The half-life is unique to each isotope and can vary widely, and is independent of external conditions.
  • Example: The half-life of Carbon-14 is 5730 years.

Rate Law Formula

• Integrated form of the first-order rate law for radioactive decay: $N_t = N_0 e^{-kt}$ where:
  • $N_t$ = the remaining quantity
  • $N_0$ = the initial quantity
  • $k$ = decay constant
  • $t$ = time

21.5 Detection of Radioactivity

• Various methods are used to detect radioactivity, including:
  1. Geiger Counters: Measure ionizing radiation via generated current.
  2. Film Badges: Measure radiation exposure based on film darkening.
  3. Scintillation Counters: Detect radiation through emitted light from phosphors.

21.6 Energy Changes in Nuclear Reactions

• The mass of a nucleus is less than the sum of the masses of its constituent nucleons, a phenomenon termed mass defect.
• The energy released or absorbed during nuclear reactions can be calculated using Einstein's formula:
  $E = mc^2$
• Binding energy per nucleon reflects the stability of a nucleus (more tightly bound nuclei are more stable).

21.7 Nuclear Power: Fission

• Fission: A heavy nucleus (like Uranium-235) splits when bombarded with neutrons, releasing large amounts of energy and producing various daughter nuclei.
• Fission reactions do not occur naturally under standard conditions but are initiated within nuclear reactors.

21.8 Nuclear Power: Fusion

• Fusion: Occurs when light nuclei fuse under high temperatures and pressures to form heavier nuclei, also releasing vast amounts of energy.
• Example in nature includes reactions within the sun.

21.9 Radiation in the Environment and Living Systems

• Ionizing radiation can cause damage to living tissues, leading to a range of health effects. The effects depend on the absorbed dose:

  • 0-25 rem: No detectable effects
  • 25-100 rem: Temporary decrease in white blood cell count
  • Beyond certain levels, severe reactions or death may occur.

• Sources of ionizing radiation include natural background radiation, medical uses, and cosmic rays.

• The penetrability of different types of radiation varies significantly, with gamma rays being the most penetrating, followed by beta particles, while alpha particles are the least penetrating but pose significant risk if ingested or inhaled.