Formula & Calculator
Radioactive Activity
Calculates the activity (decay rate) of a radioactive sample from its decay constant and the number of radioactive atoms present.
Interpretation
A = λ·N. Activity is the decay rate, proportional to the number of radioactive atoms. λ is decay constant. Unit is becquerel (Bq). Used to quantify source strength and dose.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| A | Activity | Bq (decays/s) |
| λ | Decay constant | 1/s |
| N | Number of radioactive atoms |
What it means
Activity (A) is the number of nuclear disintegrations (decays) per unit time in a radioactive sample. It is given by A = λ N, where λ is the decay constant and N is the number of radioactive nuclei. The SI unit is the becquerel (Bq), defined as one decay per second. The older unit is the curie (Ci), where 1 Ci = 3.7×10¹⁰ Bq. Activity is directly proportional to the amount of radioactive material and is used to characterise sources for medical, industrial, and research applications. It also determines the radiation dose rate and is used in radiation protection to limit exposure. Understanding activity is fundamental for nuclear medicine (dosing), waste management, and environmental monitoring.
Worked example
Radioactive Activity – Two Examples
Real‑World| Parameter | Value |
|---|---|
| λ | 1.2×10⁻⁴ s⁻¹ |
| N | 6×10²⁰ atoms |
| Parameter | Value |
|---|---|
| λ | 1.2×10⁻⁴ s⁻¹ |
| N | 1×10¹⁹ atoms |
Common mistakes
- Radioactive activity A: The number of decays per unit time – units: becquerel (Bq) = 1 decay/s.
- Decay constant λ: In 1/time – must be consistent with time units.
- Number of nuclei N: The number of radioactive atoms present.
- Activity is proportional to N: As N decreases, activity decreases exponentially.
- Specific activity: Activity per unit mass – see ID 847.
Applications
Radioactive activity (A) is the rate of decay of a radioactive substance, given by A = λ·N, where λ is the decay constant and N is the number of radioactive nuclei. It is measured in becquerels (Bq) or curies (Ci). Activity is the fundamental quantity for radiation safety, medical applications, and environmental monitoring. Health physicists use activity to assess the potential radiation dose to workers and the public, to design handling protocols, and to determine the required shielding. In nuclear medicine, the activity of a radiopharmaceutical determines the therapeutic or diagnostic dose. By measuring and calculating activity, professionals can ensure safe and effective use of radioactive materials in all applications.
- Radiation safety and dose assessment in nuclear facilities
- Calibration and use of radiation detectors (Geiger counters, scintillators)
- Design of radiopharmaceutical doses for therapy and imaging
- Environmental monitoring of radioactive contamination
- Inventory management of radioactive sources and waste
Frequently Asked Questions
Activity (A) is the rate of decay of a radioactive sample, defined as the number of decays per unit time. It is given by A = λ · N, where λ is the decay constant and N is the number of radioactive nuclei present. The SI unit is the becquerel (Bq), which is one decay per second.
Confusing activity (the decay rate) with the number of atoms or the total mass of the radioactive material. Activity depends on both the isotope (λ) and the quantity (N).
Since λ = ln(2)/T₁/₂, the activity is A = (ln(2)/T₁/₂) · N. This shows that a short half‑life (large λ) results in a higher activity for the same number of nuclei.
Activity decays exponentially: A(t) = A₀ e^(–λt), where A₀ is the initial activity. After one half‑life, the activity is halved.
SI unit is Becquerel (Bq) = 1 decay/s. Older unit is Curie (Ci): 1 Ci = 3.7×10¹⁰ Bq. Also, 1 Rutherford = 10⁶ Bq.
Specific activity is the activity per unit mass: SA = A / m = (λ·N_A) / M, where N_A is Avogadro's number, M is the molar mass. It is a measure of the intrinsic radioactivity of an isotope.
Using radiation detectors (Geiger‑Müller counter, scintillation detector, or semiconductor detector). The count rate is measured and corrected for detector efficiency and geometry to obtain the absolute activity.
Co‑60 has λ = ln(2)/5.27 years = 0.1315 y⁻¹ = 4.17×10⁻⁹ s⁻¹. Number of atoms in 1g = (1/59.93)×6.022×10²³ = 1.005×10²². Activity = λ·N ≈ 4.17×10⁻⁹ × 1.005×10²² ≈ 4.19×10¹³ Bq ≈ 1130 Ci.
Activity is the rate of decay (Bq). Dose is the energy absorbed by tissue (Gy or Sv). Activity is a source property; dose depends on the type of radiation, distance, and shielding.