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_atoms

Activity

activity_ci = lambda * num_atoms / 3.7e10

Decay Constant (lambda)

decay_const = lambda

Variables

VariableDescriptionDefault
num_atomsNumber of Radioactive Atoms (N)1000000000000000
half_life_sHalf-Life(seconds)3600
lambdaDerived value= log(2) / half_life_scalculated

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).

num_atoms = 1000000000000000half_life_s = 3600
  1. 01lambda = ln(2) / 3600 = 1.925 × 10⁻⁴ s⁻¹
  2. 02A = 1.925 × 10⁻⁴ × 10¹⁵ = 1.925 × 10¹¹ Bq
  3. 03A = 1.925 × 10¹¹ / 3.7 × 10¹⁰ = 5.20 Ci

Ready to run the numbers?

Open Activity (Becquerel) Calculator