Radioactive Activity Calculator
Computes the radioactive activity of a sample in curies from its atom count and decay constant. Use this when characterizing radioisotope sources for medical physics, nuclear waste inventory, or laboratory safety.
About this calculator
Radioactive activity measures how many decay events occur per second in a sample. The fundamental relationship is: A = N × λ, where N is the number of radioactive atoms and λ (lambda) is the decay constant in s⁻¹. The decay constant is related to half-life by λ = ln(2)/t½ ≈ 0.693/t½. This calculator converts the raw activity from becquerels (decays/s) to the more familiar curie unit by dividing by 3.7×10¹⁰, since 1 curie = 3.7×10¹⁰ Bq by definition. So the full formula is: Activity (Ci) = N × λ / 3.7×10¹⁰. This calculation is essential for preparing radiopharmaceutical doses, quantifying spent fuel isotopic inventories, and demonstrating regulatory compliance for radioactive material licenses. The number of atoms N can be derived from the sample mass using N = (mass × Nₐ) / atomic mass.
How to use
Consider a sample containing 2×10¹⁵ atoms of I-131, which has a decay constant of 9.98×10⁻⁷ s⁻¹. Step 1: Calculate activity in becquerels: A = N × λ = 2×10¹⁵ × 9.98×10⁻⁷ = 1.996×10⁹ Bq. Step 2: Convert to curies: 1.996×10⁹ / 3.7×10¹⁰ ≈ 0.054 Ci, or about 54 mCi. This is a typical diagnostic dose range for thyroid imaging, illustrating the practical relevance of this calculation in nuclear medicine settings.
Frequently asked questions
How do I find the decay constant if I only know the half-life of a radioisotope?
The decay constant λ and half-life t½ are inversely related by λ = ln(2) / t½ ≈ 0.693 / t½. You must use consistent units—if t½ is in seconds, λ will be in s⁻¹. For example, I-131 has a half-life of 8.02 days = 693,000 s, giving λ = 0.693 / 693,000 ≈ 9.99×10⁻⁷ s⁻¹. Half-life values for all radioisotopes are tabulated in the NNDC (National Nuclear Data Center) database and the IAEA's Live Chart of Nuclides, both freely available online. Always double-check units before entering values into calculations.
What is the difference between activity in becquerels and activity in curies?
Both becquerels (Bq) and curies (Ci) measure radioactive activity—the number of nuclear disintegrations per second—but they differ enormously in magnitude. One becquerel equals exactly one disintegration per second, while one curie equals 3.7×10¹⁰ disintegrations per second, originally defined as the activity of one gram of radium-226. The curie is the older, customary unit still widely used in the United States, while the becquerel is the SI unit preferred internationally and in scientific literature. For practical purposes, 1 Ci = 37 GBq; medical doses are often expressed in millicuries (mCi) or megabecquerels (MBq).
Why does activity decrease over time even if no atoms leave the sample?
Activity decreases because the number of radioactive atoms N continuously diminishes as each decay converts a radioactive nucleus into a daughter product. Since A = N × λ, and N follows exponential decay N(t) = N₀ × e^(−λt), the activity also decays exponentially: A(t) = A₀ × e^(−λt). After one half-life, both N and A are reduced by half; after two half-lives, to one quarter, and so on. This is why radiopharmaceutical doses must be calibrated to a specific date and time, and why nuclear waste repositories must plan for storage durations of many half-lives to allow activity to drop to safe levels.