Activity Calculator Formula

Understand the math behind the activity calculator. Each variable explained with a worked example.

Use the Activity Calculator

Formulas Used

Decay Constant

decay_constant = log(2) / half_life_s

Activity

activity_bq = log(2) / half_life_s * num_atoms

Activity (Ci)

activity_ci = log(2) / half_life_s * num_atoms / 3.7e10

Variables

VariableDescriptionDefault
num_atomsNumber of Atoms100000000000000000000
half_life_sHalf-Life(s)3600

How It Works

Radioactive Activity

Activity measures the rate of radioactive decays per unit time.

Formula

A = lambda * N = (ln2 / t_half) * N

where lambda is the decay constant, N is the number of atoms, and t_half is the half-life. The unit is becquerel (Bq) = 1 decay/second.

Worked Example

1 x 10^20 atoms with a half-life of 3600 s (1 hour).

num_atoms = 100000000000000000000half_life_s = 3600
  1. 01lambda = ln(2) / t_half = 0.6931 / 3600 = 1.925e-4 /s
  2. 02A = lambda * N = 1.925e-4 * 1e20
  3. 03A = 1.925e16 Bq
  4. 04A = 1.925e16 / 3.7e10 = 520,270 Ci

Ready to run the numbers?

Open Activity Calculator