type: application_note | subtopic: Applications of Radioactive Decay
Radiocarbon (^{14}C) Dating
- Principle: Carbon-14 (t_{1}/_{2} = 5730 years) is continuously produced in the atmosphere by cosmic rays and is absorbed by all living organisms.
- Process: When an organism dies, it stops absorbing ^{14}C. The ^{14}C begins to decay: ^{14}{6}C → ^{14}{7}N + + ν̄.
- Dating: By measuring the ratio of ^{14}C to ^{12}C (stable) and comparing to the atmospheric ratio, scientists calculate how long ago the organism died.
- Range: Effective for ~50,000 years (about 8–9 half-lives).
NEET application: A wooden artifact has ^{14}C activity 1/4 of a living tree. Age = 2 × t_{1}/_{2} = 2 × 5730 = 11,460 years.
Nuclear Reactors (Fission)
- U-235 or Pu-239 undergoes fission releasing ~200 MeV per event.
- Chain reaction: each fission releases 2–3 neutrons triggering further fissions.
- Moderator (heavy water, graphite) slows neutrons for more efficient capture.
- Control rods (boron, cadmium) absorb excess neutrons to control reaction rate.
Nuclear Fusion (Stars and Hydrogen Bombs)
- Stars fuse H nuclei into He: 4p → He-4 + 2 + 2ν + 26.7 MeV (proton-proton chain).
- ITER (experimental reactor): D + T → He-4 + n + 17.6 MeV.
- Conditions: extremely high temperature (~10^{8} K) to overcome Coulomb repulsion.
Medical Applications
- PET scans: positron emitters (^{18}F, t_{1}/_{2} = 110 min) for brain/tumor imaging.
- Cancer treatment: γ-ray from Co-60 (teletherapy) or I-131 (thyroid cancer).
- Bone scans: Tc-99m (t_{1}/_{2} = 6 h) for diagnostic imaging.
Hydrogen Spectrum in Astrophysics
- Stellar composition determined by spectral analysis (Balmer series most prominent in sun).
- Redshift: observed wavelengths longer than emitted → universe is expanding.
- Hydrogen 21-cm line (hyperfine transition) used to map the Milky Way.