Nuclear Chemistry: Isotopes, Isotones, and Isomers

Nuclear Chemistry

• Isotopes: atoms of the same element with different numbers of neutrons
  • Examples: 12C, 13C, 11C, 14C, 15C
  • Stable isotopes: not radioactive, e.g. 12C, 13C
  • Radioisotopes: radioactive, e.g. 11C, 14C, 15C
• Isotones: atoms of different elements with the same number of neutrons
• Isomeric state: atoms of the same element with the same number of protons, neutrons, and electrons, but different energy levels
• Radioactivity: natural elements that disintegrate to emit various rays
  • Alpha (α) rays: positive charge, affected by magnetic and electric fields, stopped in a few centimeters of air
  • Beta (β) rays: negative charge, affected by magnetic and electric fields, stopped in a few meters of air and a few millimeters of tissue
  • Gamma (γ) rays: no charge, unaffected by magnetic and electric fields, high energy photon with high penetrating power
• Radiation doses in nuclear medicine: depend on physical characteristics of the radionuclide, particles emitted, energies, and length of time in the organ
  • Effective half-life (T½eff): combination of physical half-life (T½phy) and biological half-life (T½bio)

Radionuclides in Medicine

• Most useful radionuclides emit gamma rays, which are very penetrating
• Beta particles are not very penetrating and are generally of little use for diagnosis
• Exceptions: 3H and C14 play important roles in medical research, and 32P is used for diagnosis of tumors in the eye
• Short-lived gamma-emitting radionuclides of common organic elements (C, N, O) are difficult to use in clinical medicine without an accelerator

Radioactive Decay

• Each radionuclide decays at a fixed rate, commonly indicated by the half-life (T½)
• Basic equation describing radioactive decay: A = Ao e–λ t
• Decay constant (λ) and half-life (T½) are related: T½ = 0.693 / λ
• Units of radioactivity: curie (Ci), where 1 Ci = 3.7*10^10 disintegrations per second
  • Subunits: mCi, μCi, nCi, pci
• SI unit for radioactivity: Becquerel (Bq), where 1 Bq = 1 disintegration per second
  • Subunits: KBq, MBq, GBq

Blackbody Radiation Laws

• Ideal blackbody: absorbs all incident radiation, and none is reflected or transmitted
• Energy output of a blackbody is a function of its temperature and is not spread uniformly across all wavelengths
• Stefan-Boltzmann law: total radiant heat output emitted from a surface is proportional to its absolute temperature to the fourth power (E = eσAT^4)
• Planck's law: relation for the spectral blackbody emissive power, assuming radiation originates from oscillating atoms
• Wein's displacement law: peak of the radiation curve shifts to shorter wavelengths as temperature rises, used to calculate temperatures of hot radiant objects like stars
• Observations from blackbody radiation graph:
  • Curves shift to shorter wavelengths as temperature rises
  • Greater proportion of radiation is emitted at shorter wavelengths at higher temperatures