How It Works
Activity (A) is the rate of radioactive disintegrations per second in a sample. It is the product of the decay constant and the number of radioactive atoms present: A = λN. The SI unit is the becquerel (Bq), defined as one disintegration per second. The older curie (Ci) equals 3.7 × 10¹⁰ Bq — the activity of one gram of radium-226. Activity decreases exponentially over time at the same rate as the number of atoms.
Example Problem
A sample contains 1.0 × 10²⁰ atoms of a radioactive isotope with decay constant λ = 0.001 s⁻¹. Calculate the activity in becquerels and curies.
- Use A = λN. Substitute the given values.
- A = 0.001 s⁻¹ × 1.0 × 10²⁰ atoms.
- A = 1.0 × 10¹⁷ disintegrations per second = 1.0 × 10¹⁷ Bq.
- Convert to curies: 1.0 × 10¹⁷ Bq ÷ 3.7 × 10¹⁰ Bq/Ci ≈ 2.7 × 10⁶ Ci.
- Interpretation: this sample emits 10¹⁷ particles per second — millions of curies, an extremely active source.
Key Concepts
Activity is what radiation detectors measure directly; mass-to-mass comparisons of radioactive samples are deceptive because one gram of a short-lived isotope can be enormously more active than one gram of a long-lived isotope with the same atomic structure. Activity scales linearly with the number of atoms (N) and inversely with half-life (small t½ → large λ → large A). Because A = λN and N decays exponentially, activity itself follows A(t) = A₀e^(-λt). Specific activity (Bq per gram) is a useful normalized quantity for comparing isotopes.
Applications
- Nuclear medicine — radiopharmaceutical dose is specified in MBq or mCi at calibration time and back-calculated to administration time using the half-life.
- Radiation safety — exposure limits are set in terms of activity per unit area or volume, not mass.
- Smoke detector design — the 0.9 µCi americium-241 button in residential detectors emits alpha particles to ionize the air gap.
- Industrial radiography — Ir-192 sources (typically 1–100 Ci) image welds in pipelines and pressure vessels.
- Environmental monitoring — bequerels per kg of soil or per liter of water benchmark contamination levels after nuclear releases.
Common Mistakes
- Confusing activity with dose — activity counts disintegrations; dose (Gy, Sv) accounts for energy absorbed and biological weighting.
- Forgetting that activity decreases with time — a medical isotope's activity at administration is lower than at calibration; correct using A(t) = A₀ e^(-λt).
- Using mixed units — if N is in atoms and λ is in s⁻¹, A comes out in Bq; if λ is in min⁻¹, multiply by 1/60 to get Bq.
- Equating curies and becquerels — 1 Ci = 3.7 × 10¹⁰ Bq; orders of magnitude apart.
Frequently Asked Questions
How do you calculate radioactive activity?
Multiply the decay constant by the number of radioactive atoms: A = λN. The result is in becquerels (decays per second) when λ is in s⁻¹.
What is the formula for activity?
A = λN. Equivalently, since λ = ln(2)/t½, you can write A = N × ln(2) / t½ — useful when the half-life is given instead of the decay constant.
What units is activity measured in?
The SI unit is the becquerel (Bq), one decay per second. The older curie (Ci) equals 3.7 × 10¹⁰ Bq and is still widespread in medical and nuclear industry contexts. Submultiples kBq, MBq, GBq and mCi, µCi are common.
How is activity different from radiation dose?
Activity tells you how many disintegrations are happening per second; dose tells you how much energy is being absorbed per unit mass of tissue (gray, Gy) and how much biological harm that energy does (sievert, Sv). A high-activity source far away may deliver less dose than a lower-activity source held in your hand.
What is specific activity?
Specific activity is activity divided by mass — typically expressed in Bq/g or Ci/g. It's a property of the isotope (and any carrier isotopes), useful for comparing samples of different sizes or estimating how much mass a given activity represents.
Does activity stay constant over time?
No — activity decreases exponentially at the same rate as the number of atoms, since A = λN. A freshly produced medical isotope is far more active than the same physical sample after a few half-lives.
Reference: Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.
Related Calculators
- Half-Life Calculator — t½ = ln(2)/λ — derive λ from a published half-life
- Mean Lifetime Calculator — τ = 1/λ — average atom survival time
- Radioactive Decay Calculator — N(t) = N₀ e^(−λt) — quantity vs. time
- Radioactive Material Calculator — the full four-equation hub for decay problems
- Power Calculator — compute decay heat from activity and per-decay energy
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