Throughout all the chemical reactions studied so far, one law remained absolute: Dalton’s atomic conservation. Atoms exchanged valence electrons or formed covalent bonds, but a carbon atom entered every reaction as carbon and emerged as carbon. Inside an unstable atomic nucleus, that rule is obliterated. Driven by repulsive electrostatic forces overpowering the residual strong force, unstable isotopes eject matter and energy to transmute into entirely new elements. Whether through the steady, clockwork ticking of radioactive decay that dates Egyptian mummies or the cataclysmic energy release of nuclear fission that powers cities, nuclear processes operate under conservation laws governed not by chemistry, but by mass defect and the binding energy of the nucleus.
In chemical reactions, atoms rearrange their valence electron bonds while atomic nuclei remain untouched. In nuclear reactions, the nucleus itself changes composition. To write and balance nuclear equations, scientists use standard nuclear-notation:
A nuclear equation is balanced if and only if both totals match exactly on both sides:
When an atomic nucleus has an unstable ratio of neutrons to protons, or is simply too massive to remain bound, it spontaneously decays by emitting ionizing particles or radiant photons:
Heavy nuclei (Z > 82) shed excess mass by ejecting an alpha particle: a tightly bound helium-4 nucleus (42He).
23892U → 23490Th + 42He
Result: Mass number drops by 4; atomic number drops by 2 (transmuting uranium into thorium).
In nuclei with too many neutrons, the weak nuclear force transforms a neutral neutron into a positive proton, ejecting a high-speed electron (0−1e) and an antineutrino (ν̄e):
146C → 147N + 0−1e + ν̄e
Result: Mass number A stays identical (14); atomic number Z increases by 1 (carbon becomes nitrogen).
Following alpha or beta decay, the daughter nucleus is often left in an excited, metastable nuclear state (*). It sheds this excess energy by emitting an extremely high-frequency photon:
99m43Tc → 9943Tc + 00γ
Result: Zero change in mass or atomic number; pure electromagnetic energy.
If you hold a single atom of radioactive Carbon-14, it is impossible to predict when it will decay. It might decay five seconds from now, or 20,000 years from now. But if you hold a sample of 1 trillion Carbon-14 atoms, quantum statistics guarantee that exactly half of them will decay every 5,730 years.
The half-life (t1/2) is the constant time required for exactly 50% of the radioactive nuclei in a sample to undergo decay. Because nuclear decay is completely shielded from external chemistry, temperature, pressure, and chemical bonding, half-lives act as immutable geological clocks:
Investigate both spontaneous radioactive decay and induced nuclear fission chain reactions. Toggle between the decay workbench and the nuclear fission reactor simulator below.
Test your ability to balance nuclear transmutations and calculate half-life decay kinetics before attempting the constructed response exam task.
In chemical reactions, heating a reactant accelerates the reaction rate, while chemical bonding alters reactivity. However, boiling Carbon-14 in acid or subjecting it to 100,000 atmospheres of pressure produces zero change in its half-life (5,730 years). Explain at the subatomic scale why radioactive decay rates are immune to external chemical and physical conditions.
Archaeologists excavating an ancient burial site in the Mediterranean discover a wooden funerary chest.
A 1.00-gram carbon sample extracted from the wooden chest undergoes radiocarbon dating. In living trees, Carbon-14 decays at an activity of 16.0 counts per minute (cpm) per gram of carbon.
The 1.00-gram sample from the ancient chest registers an activity of 2.0 counts per minute (cpm).
The half-life of Carbon-14 (146C) is 5,730 years.
(a) Write the complete, balanced nuclear equation for the radioactive decay of Carbon-14 into its stable daughter isotope. [1 mark]
(b) Calculate the number of half-lives that have elapsed since the tree was harvested, and determine the age of the wooden chest in years. [2 marks]
(c) Explain why radiocarbon dating cannot be used to date a dinosaur bone that is 68 million years old, and propose an alternative radiometric isotope system suitable for dating geological rocks of that age. [1 mark]
Self-score: 4 = correct equation, precise 3 half-life and 17,190-year math, and clear justification of carbon dating limits with a valid geological isotope system · 3 = minor calculation error · 2 = parts (a) and (b) correct only · ≤1 = incomplete responses without nuclear principles.
Radioactive decay is one of medicine’s most formidable weapons against cancer. In targeted alpha therapy (TAT), short-lived alpha-emitting isotopes like Actinium-225 or Radium-223 are bonded to monoclonal antibodies tailored to lock onto cancer cell receptors. Because alpha particles have high mass and electric charge (+2), they travel less than 50 micrometers, the diameter of just a few cells, delivering lethal, double-strand DNA damage directly inside the malignant tumor while leaving surrounding healthy tissue unharmed.