Nuclear chemistry (advanced)
The idea
Nuclear chemistry follows the nucleus rather than the electron cloud. Unstable isotopes decay by characteristic modes — alpha emission (helium-4 nucleus, common for heavy elements), beta-minus (a neutron becomes a proton, ejecting an electron), positron emission and electron capture (proton becomes neutron), and gamma release of excess energy. Balancing a nuclear equation means conserving mass number and atomic number across the arrow; chemistry's usual bookkeeping of bonds and charges is irrelevant here because the electron shells are bystanders.
Every radioactive decay is kinetically first order, so the tools you built for kinetics transfer wholesale: a constant half-life t½, a decay constant k = 0.693/t½, and the age-dating workhorse t = (1/k)·ln(N₀/N). Radiocarbon dating exploits this: living tissue maintains a steady carbon-14 fraction, the clock starts at death, and the remaining fraction reveals elapsed time. Mass–energy bookkeeping via E = mc² explains why nuclear processes dwarf chemical ones — fission and fusion convert measurable mass defects into millions of times more energy per gram than combustion.
Discard the intuition that two half-lives finish the job: each half-life removes half of whatever remains, so 25% survives after two and the decay tail stretches on exponentially. And because decay is a nuclear event, temperature, pressure, and chemical bonding leave its rate untouched.
Worked example
Carbon-14 undergoes beta-minus decay with a half-life of 5730 years. Write the nuclear equation, then find the age of a wooden artifact whose carbon-14 activity is 35% of that found in living wood.
- Balance the decay: ¹⁴C → ¹⁴N + β⁻. The mass number stays 14 while the atomic number rises from 6 to 7, because a neutron inside the nucleus converted into a proton plus the emitted electron.
- Convert the half-life to a decay constant: k = 0.693/5730 = 1.21 × 10⁻⁴ yr⁻¹.
- Apply the first-order clock with the surviving fraction N/N₀ = 0.35: t = (1/k)·ln(N₀/N) = ln(1/0.35)/(1.21 × 10⁻⁴) = 1.050/(1.21 × 10⁻⁴) ≈ 8680 years.
- Sanity-check against whole half-lives: one half-life (5730 yr) would leave 50% and two (11,460 yr) would leave 25%; the measured 35% sits between them, and 8680 years lands neatly between the two times — about 1.5 half-lives, since 0.5^1.5 ≈ 0.354.
Answer. The decay is ¹⁴C → ¹⁴N + β⁻, and the artifact is about 8700 years old (8.7 × 10³ yr).
Check your understanding
- Why does beta-minus decay raise the atomic number while leaving the mass number fixed, and which conservation laws enforce that?
- What assumptions about atmospheric carbon-14 does radiocarbon dating rely on, and how would a violation bias the computed age?
- Why is the energy released per gram in fission so much larger than in combustion, and where does that energy physically come from?
- How would you decide whether an unstable isotope is likely to decay by beta emission versus positron emission from its neutron-to-proton ratio?
Build the foundations first
Nuclear chemistry (advanced) builds on these concepts. If any feel shaky, start there.