Atomic and Nuclear Structure · 3 min read
Radioactivity and Half-Life
Radioactivity is the spontaneous emission of particles or energy from an unstable nucleus. Stability depends on the neutron-to-proton ratio: light stable nuclei have about equal numbers of neutrons and protons, heavier stable nuclei need more neutrons than protons, and every nucleus with more than 83 protons is radioactive. An unstable nucleus decays toward a more stable ratio, often through a series of steps that ends at a stable isotope, such as the uranium-238 series
ALPHA, BETA, AND GAMMA RADIATION Radiation Identity and symbol Charge
High: thick lead or concrete
No change in A or Z; releases energy
Alpha particles have the greatest ionizing ability because they are massive and doubly charged, but the least penetration. They are harmless outside the body yet dangerous if an alpha emitter is inhaled or swallowed. Gamma rays penetrate most because they have no mass or charge, and they usually accompany alpha or beta decay as the new nucleus drops to a lower energy state. In an electric field, alpha particles bend toward the negative plate, beta particles bend more sharply toward the positive plate, and gamma rays pass straight through.
In every nuclear equation, the sum of mass numbers and the sum of atomic numbers are each the same on both sides. To find an unknown product, subtract, then use the new atomic number to identify the element. For alpha decay of uranium- 238: ²³⁸₉₂U → ⁴₂He + ²³⁴₉₀Th. For beta decay of carbon-14: ¹⁴₆C → ⁰₋₁e + ¹⁴₇N. The element always changes in alpha and beta decay because Z changes; it never changes in gamma emission.
Polonium-210 (Z = 84) emits an alpha particle. Identify the product. Write the equation: ²¹⁰₈₄Po → ⁴₂He + X, where X has unknown mass number A and atomic number Z.
The half-life (t½) is the time for half of the nuclei in a sample to decay. It is constant for each isotope and is not changed by temperature, pressure, or chemical combination. After n half-lives, the fraction remaining is (½)ⁿ: one-half, one- quarter, one-eighth, one-sixteenth. Decay is random for any single nucleus, so half-life describes large populations only. A graph of remaining nuclei against time is an exponential decay curve that approaches zero but never reaches it.
Half remains after 1 half-life
Each half-life cuts the remaining undecayed nuclei in half: 100% → 50% → 25% → 12.5% → 6.25%. The curve is exponential and never reaches zero.
A common error is assuming the whole sample is gone after two half-lives. Another is thinking that heating or dissolving a radioactive compound speeds its decay; nuclear decay rates do not depend on chemical or physical
Radiometric dating compares the amount of a parent isotope with what was originally present. Carbon-14 (t½ ≈ 5730 years) dates once-living material up to about 50,000 years old: living organisms keep a steady carbon-14 ratio by exchanging carbon with the environment, and the ratio falls after death. Potassium-40 and uranium-238, with half-lives of billions of years, date rocks. Other uses include cobalt-60 for cancer therapy and food irradiation, iodine-131 for thyroid treatment, technetium-99m for medical imaging, and americium-241 in smoke detectors. Hazards come from ionization that damages DNA; protection relies on time, distance, and shielding.
A 80.0 g sample of an isotope has a half-life of 5.0 days. How much remains after 15 days? A bone has 25% of its
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