Activity (Becquerel) Calculator Formula
Understand the math behind the activity (becquerel) calculator. Each variable explained with a worked example.
Formulas Used
Activity
activity_bq = lambda * num_atomsActivity
activity_ci = lambda * num_atoms / 3.7e10Decay Constant (lambda)
decay_const = lambdaVariables
| Variable | Description | Default |
|---|---|---|
num_atoms | Number of Radioactive Atoms (N) | 1000000000000000 |
half_life_s | Half-Life(seconds) | 3600 |
lambda | Derived value= log(2) / half_life_s | calculated |
How It Works
Radioactive Activity
Activity is the rate of radioactive disintegrations per second. One Becquerel (Bq) equals one disintegration per second.
Formula
A = lambda × N = (ln2 / t½) × N
where lambda is the decay constant and N is the number of radioactive atoms. The older unit Curie: 1 Ci = 3.7 × 10¹⁰ Bq (the activity of 1 gram of Ra-226).
Worked Example
10¹⁵ atoms of an isotope with half-life 3600 seconds (1 hour).
- 01lambda = ln(2) / 3600 = 1.925 × 10⁻⁴ s⁻¹
- 02A = 1.925 × 10⁻⁴ × 10¹⁵ = 1.925 × 10¹¹ Bq
- 03A = 1.925 × 10¹¹ / 3.7 × 10¹⁰ = 5.20 Ci
Frequently Asked Questions
What is the practical difference between Bq and Ci?
Bq is the SI unit (1 disintegration/second). Ci is the traditional unit (3.7 × 10¹⁰ Bq). Medical doses are often in MBq or mCi. Environmental levels are in Bq/kg or pCi/L.
How many atoms are in 1 Ci of a substance?
N = A / lambda = 3.7 × 10¹⁰ × t½ / ln(2). For Tc-99m (t½ = 6h): N = 3.7 × 10¹⁰ × 21600 / 0.693 = 1.15 × 10¹⁵ atoms, which is about 0.2 nanograms.
Does specific activity depend on isotope?
Yes. Specific activity (Bq/g) = lambda × NA / M, where NA is Avogadro number and M is atomic mass. Short-lived isotopes have enormous specific activity. Carrier-free isotopes have the maximum specific activity.
Ready to run the numbers?
Open Activity (Becquerel) Calculator