Calculate remaining quantity, half-life, decay constant, activity, and time elapsed for radioactive isotopes with visual decay curves and dose estimation.
Radioactive decay is the spontaneous transformation of an unstable atomic nucleus into a more stable configuration through the emission of particles or electromagnetic radiation. The process follows first-order kinetics: the rate of decay is proportional to the number of atoms present, leading to the characteristic exponential decay curve N(t) = N₀ × e^(−λt), where λ is the decay constant.
The half-life (t₁/₂ = ln 2 / λ) is the time for half the atoms in a sample to decay. Half-lives of known isotopes span an extraordinary range — from fractions of a microsecond (⁸Be: 6.7 × 10⁻¹⁷ s) to billions of years (²³⁸U: 4.47 × 10⁹ yr). The activity (A = λN), measured in becquerels (Bq, decays/s) or curies (Ci), quantifies how "radioactive" a sample is and is crucial for radiation safety, medical dosimetry, and nuclear waste management.
This calculator handles all common radioactive decay computations: remaining mass or atoms, activity at any time, time to reach a target activity, and conversion between decay constant, half-life, and mean lifetime. It includes presets for medically and industrially important isotopes and provides visual decay curves with safety context.
This calculator instantly computes decay for any isotope — from medical physics dosimetry to nuclear waste planning to archaeology. No memorizing formulas: enter your values and get activity, remaining mass, and decay curves. This radioactive decay calculator helps you compare outcomes quickly and reduce avoidable mistakes when making day-to-day care decisions. Use the estimate as a planning baseline and confirm final decisions with a qualified professional when risk is high.
N(t) = N₀ × e^(−λt) = N₀ × (1/2)^(t/t₁/₂), where λ = ln(2)/t₁/₂ (decay constant), A = λN (activity), τ = 1/λ (mean lifetime). Activity: A(t) = A₀ × e^(−λt). Half-life: t₁/₂ = ln(2)/λ = 0.693/λ.
Result: Remaining activity = 92.5 MBq (12.5%)
Tc-99m has t₁/₂ = 6.01 hours. After 12 hours (≈2 half-lives): A = 740 × (1/2)^(12/6.01) = 740 × 0.125 = 92.5 MBq. Two half-lives reduce activity to one-quarter.
Alpha decay emits a helium-4 nucleus, reducing the atomic number by 2 and mass number by 4. It's common in heavy elements (Z > 82) and produces highly ionizing but short-range radiation. Beta-minus decay converts a neutron to a proton, emitting an electron and antineutrino. Electron capture and beta-plus decay convert a proton to a neutron. Gamma emission accompanies other decay modes, releasing excess nuclear energy as electromagnetic radiation. Understanding these modes is essential for predicting daughter products and radiation hazards.
Nuclear medicine uses radioactive isotopes (radiopharmaceuticals) for both diagnosis and therapy. The ideal diagnostic isotope has a short half-life (hours), emits gamma rays detectable by cameras, and clears the body quickly — Tc-99m (t₁/₂ = 6 h) is the workhorse. For therapy, longer-lived isotopes that emit beta particles (I-131 for thyroid, Lu-177 for neuroendocrine tumors) deliver localized radiation dose to kill cancer cells while minimizing whole-body exposure.
Managing radioactive waste requires understanding decay timelines. Short-lived fission products (Cs-137, Sr-90, t₁/₂ ≈ 30 yr) dominate hazards for the first few centuries. Long-lived actinides (Pu-239, t₁/₂ = 24,100 yr) require geological-timescale isolation. The challenge of nuclear waste disposal is fundamentally a half-life problem: ensuring containment for enough half-lives that activity drops to background levels, which for some isotopes means hundreds of thousands of years.
Half-life is when 50% has decayed; mean lifetime (τ = t₁/₂/ln 2 ≈ 1.443 × t₁/₂) is the average time a single atom survives. They're related by a factor of ln 2.
Activity (A) is the number of decays per second. 1 Becquerel (Bq) = 1 decay/s. 1 Curie (Ci) = 3.7 × 10¹⁰ Bq. Activity depends on both the amount of material and the decay constant.
A common rule of thumb is 10 half-lives reduces activity to ~0.1% (1/1024). For waste disposal, the specific isotope and required clearance level determine the actual storage time needed.
Nuclear decay is essentially independent of external conditions (temperature, pressure, chemical state). Only extreme conditions (stellar interiors, bound-state beta decay) have measurable effects. This is why nuclear waste remains radioactive for so long.
Alpha: emits ⁴He nuclei (heavy, short range). Beta: emits electrons/positrons (moderate penetration). Gamma: emits high-energy photons (highly penetrating). Many isotopes undergo multiple decay modes in sequence.
Tc-99m is the most common diagnostic isotope (bone scans, cardiac imaging). I-131 treats thyroid cancer. F-18 (FDG-PET) images metabolic activity. Short half-lives minimize patient radiation exposure.