Half-Life
Half-life (t₁/₂) is the time required for exactly half of the radioactive atoms in a sample to undergo decay, reducing the number of undecayed nuclei to 50% of the original count. It is a constant property of each radioactive isotope, independent of temperature, pressure, or chemical state, ranging from microseconds for highly unstable nuclei to billions of years for stable isotopes. Half-life is essential in radiometric dating, nuclear medicine dosage, and radioactive waste management.
Key Formula
t₁/₂ = ln(2) / λ = 0.693 / λ
LaTeX: t_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{\lambda}
| Symbol | Meaning | Unit |
|---|---|---|
| t₁/₂ | Half-life | s (or any time unit) |
| λ | Decay constant | s⁻¹ |
| ln 2 | Natural logarithm of 2 | ≈ 0.6931 |
Worked Example
Problem
Carbon-14 has a half-life of 5730 years. A wooden artifact contains only 25% of the original C-14 activity. How old is the artifact?
Solution
Step 1: Determine how many half-lives have elapsed. If 25% remains, the sample has gone through two half-lives (100% → 50% → 25%). Step 2: Number of half-lives n = 2. Step 3: Age = n × t₁/₂ = 2 × 5730 years.
Answer
The artifact is approximately 11,460 years old.
Half-Lives of Selected Radioactive Isotopes
| Isotope | Element | Half-Life | Decay Type | Application |
|---|---|---|---|---|
| Carbon-14 | Carbon | 5,730 years | Beta-minus | Archaeological dating |
| Uranium-238 | Uranium | 4.47 × 10⁹ years | Alpha | Geological dating |
| Iodine-131 | Iodine | 8.02 days | Beta-minus | Thyroid cancer treatment |
| Technetium-99m | Technetium | 6.01 hours | Gamma | Medical imaging |
| Polonium-214 | Polonium | 164 microseconds | Alpha | Research only |
Interactive Tools
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Related Terms
Radioactive Decay
Radioactive decay is the spontaneous transformation of an unstable atomic nucleus into a more stable configuration by emitting radiation in the form of particles or electromagnetic waves. This process occurs because the nucleus has too many protons, too many neutrons, or excess energy, making it thermodynamically unstable. It is the foundation of nuclear medicine, radiometric dating, and nuclear power generation.
Alpha Decay
Alpha decay is a type of radioactive decay in which an unstable nucleus emits an alpha particle — a helium-4 nucleus consisting of two protons and two neutrons — thereby reducing its atomic number by 2 and its mass number by 4. This process is common in heavy nuclei (Z > 82) such as uranium and radium, where the nuclear repulsion between protons becomes too great to maintain stability. Alpha particles have low penetrating power and can be stopped by a sheet of paper, but are highly ionising and dangerous if ingested or inhaled.
Nuclear Binding Energy
Nuclear binding energy is the energy required to completely separate a nucleus into its individual protons and neutrons, or equivalently, the energy released when these nucleons combine to form the nucleus. It arises from the strong nuclear force overcoming electromagnetic repulsion between protons, and is directly related to the mass defect — the difference between the mass of the nucleus and the sum of masses of its constituent nucleons via Einstein's E = mc². The binding energy per nucleon peaks around iron-56, explaining why both fusion of light nuclei and fission of heavy nuclei can release energy.
The term "half-life" (German: "Halbwertszeit") was introduced in 1907 by Ernest Rutherford to describe the characteristic time scale of radioactive decay, derived from the mathematical property of exponential decay where half the quantity disappears in each period.