Nuclear Chemistry and Radioactivity: Decay, Half-Life, and Nuclear Reactions

Henri Becquerel Left Uranium on a Photographic Plate — and Changed Physics

In February 1896, French physicist Henri Becquerel stored uranium salts on top of unexposed photographic plates in a drawer, planning to test his hypothesis that phosphorescent materials emit X-rays when activated by sunlight. Paris was overcast, so the experiment was never conducted — but when Becquerel developed the plates anyway, he found they were fogged. The uranium had emitted radiation spontaneously, without sunlight or any external activation. This was the accidental discovery of radioactivity. Within two years, Marie and Pierre Curie had identified two new radioactive elements — polonium and radium — and established that radioactivity was an atomic property, not a molecular or crystalline one. Nuclear chemistry was born.

The Structure of the Nucleus

The atomic nucleus consists of protons (positively charged) and neutrons (electrically neutral), collectively called nucleons, bound together by the strong nuclear force — the strongest of the four fundamental forces, but with a range of only about 1–3 femtometers (10⁻¹⁵ m). A nucleus is characterized by its atomic number Z (number of protons, determines the element) and mass number A (total nucleons). Isotopes are atoms of the same element with different numbers of neutrons.

Nuclear stability depends on the proton-to-neutron ratio. For light nuclei, stability requires roughly equal numbers (Z ≈ N). For heavier nuclei, neutrons must outnumber protons to offset the electrostatic repulsion between protons. The "valley of stability" on a chart of nuclides marks which isotope combinations are stable; nuclei outside this valley are radioactive.

Types of Radioactive Decay

Half-Life: The Clock of Radioactive Decay

Radioactive decay is a stochastic quantum process — any individual nucleus may decay at any moment, with a fixed probability per unit time. For a large population of identical radioactive nuclei, the number remaining decreases exponentially:

N(t) = N₀ × e⁻λt = N₀ × (1/2)^(t/t½)

where λ is the decay constant and t½ = ln2/λ ≈ 0.693/λ is the half-life — the time for half the nuclei to decay. Half-lives span an enormous range:

• Polonium-214: t½ = 164 microseconds
• Iodine-131: t½ = 8.02 days (used in thyroid cancer treatment)
• Cesium-137: t½ = 30.2 years (Chernobyl and Fukushima concern)
• Carbon-14: t½ = 5,730 years (basis of radiocarbon dating)
• Uranium-238: t½ = 4.47 × 10⁹ years (comparable to Earth's age)

Radiocarbon dating exploits the known half-life of ¹⁴C to determine the age of organic materials up to ~50,000 years old. ¹⁴C is continuously produced in the upper atmosphere by cosmic ray bombardment of nitrogen-14: ¹⁴N + n → ¹⁴C + p. Living organisms maintain a constant ¹⁴C/¹²C ratio by exchanging carbon with the environment. After death, the ratio declines exponentially with the 5,730-year half-life.

Nuclear Fission

Nuclear fission is the splitting of a heavy nucleus into two smaller nuclei (fission fragments) plus typically 2–3 neutrons and energy. The reaction is initiated when a nucleus like uranium-235 or plutonium-239 absorbs a neutron:

²³⁵U + n → ²³⁶U* → ⁹²Kr + ¹⁴¹Ba + 3n + ~200 MeV

The released neutrons can trigger additional fissions in a chain reaction. In a nuclear reactor, the chain reaction is controlled (each fission produces on average exactly one further fission, k = 1); in an atomic bomb, it is supercritical (k > 1) and exponentially accelerating. The 200 MeV per fission event — compared to ~4 eV per chemical reaction — explains why uranium fuel is roughly 50 million times more energy-dense than coal by mass.

Nuclear Fusion

Nuclear fusion combines light nuclei into heavier ones, releasing even more energy per unit mass than fission. The Sun generates energy through the proton-proton chain, ultimately fusing four hydrogen nuclei into one helium nucleus:

4 ¹H → ⁴He + 2e⁺ + 2νe + 2γ + 26.7 MeV

The most accessible fusion reaction for terrestrial reactors combines deuterium (²H) and tritium (³H):

²H + ³H → ⁴He + n + 17.6 MeV

Fusion requires temperatures of ~100 million Kelvin to overcome the electrostatic repulsion between nuclei. ITER (International Thermonuclear Experimental Reactor), under construction in France, aims to demonstrate fusion ignition — producing more energy than the heating input requires — by the late 2020s.

Radiation Effects and Biological Safety

Ionizing radiation damages biological tissue by breaking chemical bonds, particularly in DNA. The severity depends on the dose (measured in gray, Gy = J/kg of tissue), the radiation type (characterized by a quality factor), and which organs are exposed. The effective dose in sieverts (Sv) accounts for both dose and biological effectiveness:

• Background radiation: ~3 mSv/year (varies by location; elevated near granite geology)
• Chest X-ray: ~0.1 mSv
• Transatlantic flight: ~0.08 mSv
• CT scan: ~5–20 mSv
• Acute radiation syndrome threshold: ~1,000 mSv (1 Sv)
• Lethal dose (50% in 30 days, no treatment): ~4–5 Sv

Nuclear medicine exploits radioactivity for diagnosis and therapy. PET scans use fluorine-18-labeled glucose to image metabolically active tissues. Iodine-131 therapy selectively destroys thyroid tissue (malignant or overactive) because the thyroid specifically concentrates iodine. Technetium-99m, with a 6-hour half-life and pure gamma emission, is the most widely used radioisotope in medical imaging, used in about 80% of all nuclear medicine diagnostic procedures worldwide.