Nuclear chemistry
Some nuclei are unstable and change into other elements by emitting radiation. Nuclear processes power the Sun, date ancient objects, and treat disease.
Radioactivity
Unstable nuclei decay spontaneously, emitting radiation. Alpha decay emits a helium nucleus (\(^4_2\text{He}\)), reducing \(A\) by 4 and \(Z\) by 2. Beta-minus decay turns a neutron into a proton, emitting an electron, so \(Z\) rises by 1. Gamma decay emits high-energy light without changing \(A\) or \(Z\).
Balancing nuclear equations
Mass numbers and atomic numbers must balance on both sides. Uranium-238 alpha decay: \(^{238}_{92}\text{U} \to ^{234}_{90}\text{Th} + ^4_2\text{He}\). Check: \(238 = 234 + 4\) and \(92 = 90 + 2\).
^{238}_{92}\text{U} \to ^{234}_{90}\text{Th} + ^{4}_{2}\text{He}Half-life
The half-life is the time for half of a radioactive sample to decay. After \(n\) half-lives, \(\left(\frac{1}{2}\right)^n\) remains. Iodine-131, used in thyroid treatment, has a half-life of about 8 days, so after 24 days one-eighth remains. Half-lives range from fractions of a second to billions of years.
Radiocarbon dating
Living things maintain a steady ratio of carbon-14 to carbon-12. After death, carbon-14 decays with a half-life of about 5,730 years. Measuring the remaining fraction dates organic remains up to roughly 50,000 years old. A sample with one-quarter of the living ratio is about \(2 \times 5730 \approx 11{,}460\) years old.
Fission
In nuclear fission, a heavy nucleus such as uranium-235 absorbs a neutron and splits into smaller nuclei, releasing energy and more neutrons that can trigger a chain reaction. Nuclear power plants control this chain reaction to produce heat for electricity.
Fusion
In nuclear fusion, light nuclei combine into heavier ones, releasing even more energy per kilogram. The Sun fuses hydrogen into helium. Fusion requires extreme temperatures and pressures; researchers are working to achieve sustained, net-energy fusion on Earth.
Mass-energy equivalence
The products of fission and fusion weigh slightly less than the reactants. The missing mass becomes energy according to \(E = mc^2\). Because \(c^2\) is enormous, a tiny mass loss releases vast energy, which is why nuclear fuel is so energy-dense.
E = mc^2Radiation and health
Ionising radiation can damage DNA. It is used deliberately to kill cancer cells in radiotherapy and to sterilise medical equipment. Exposure is limited by time, distance, and shielding: alpha particles are stopped by paper, beta by aluminium, and gamma rays require thick lead or concrete.
Key takeaways
Alpha decay lowers \(A\) by 4 and \(Z\) by 2; beta-minus raises \(Z\) by 1; gamma changes neither. Balance mass and atomic numbers in nuclear equations. After \(n\) half-lives, \((1/2)^n\) remains, the basis of radiocarbon dating. Fission and fusion release energy from mass via \(E = mc^2\).
Flashcard
^4_2\text{He}
Check your understanding
A radioactive isotope has a half-life of 10 days. What fraction remains after 30 days?