Radioactive Activity: Becquerel and Curie Units Explained
Activity tells us how many nuclei in a radioactive sample decay every second. It is the practical measure of how radioactive something is — how strong a source is right now. A sample can contain many atoms but have low activity if its decay constant is tiny.
Doctors, reactor engineers, and safety officers quote activity, not atom counts, because activity directly relates to radiation dose and detector counts.
Key Concepts
- Activity (A or R): number of disintegrations per second.
- Becquerel (Bq): SI unit; 1 Bq = 1 decay per second.
- Curie (Ci): older unit; 1 Ci = 3.7 × 10¹⁰ Bq, originally the activity of 1 gram of radium-226.
Formulas
A = λN, where A is in Bq, λ in s⁻¹, N is the number of undecayed nuclei. Over time: A = A₀ e^(−λt), decaying with the same half-life as N. Also A₀ = λN₀.
Worked Example
A sample has N = 3.0 × 10¹⁸ nuclei of an isotope with half-life 6 hours. Find its activity in Bq and Ci.
- λ = 0.693 / T½ = 0.693 / (6 × 3600 s) = 0.693 / 21600 = 3.21 × 10⁻⁵ s⁻¹.
- A = λN = 3.21 × 10⁻⁵ × 3.0 × 10¹⁸ = 9.63 × 10¹³ Bq.
- In curies: 9.63 × 10¹³ / 3.7 × 10¹⁰ = 2,603 Ci.
Common Misconceptions
- Students think activity and number of atoms are the same. A depends on both N and λ; a long-lived isotope has low activity even with many atoms.
- Many think curie is the SI unit. The SI unit is the becquerel; curie is a legacy unit still used in medicine in some countries.
- Some believe activity measures energy. It counts decays per second; energy per decay is a separate quantity.
Real-World Applications
Activity labelling on medical tracers, calibrating radiotherapy sources, setting safety limits for workers, checking food contamination after nuclear accidents, and certifying smoke-detector sources all use becquerels.
To picture the becquerel, a typical banana has an activity of about 15 Bq from potassium-40 — completely harmless because the energy involved is tiny and the body regulates potassium. A hospital tracer dose, on the other hand, may be hundreds of millions of becquerels (megabecquerels, MBq) so that gamma cameras can form an image quickly, and it decays away within hours. Always quote activity with the isotope name, because the same activity of different isotopes can mean very different doses.
Remember: activity A = λN decays per second, measured in becquerel (SI) or curie (1 Ci = 3.7 × 10¹⁰ Bq), and it falls exponentially just like N.