Activity Calculator Formula
Understand the math behind the activity calculator. Each variable explained with a worked example.
Formulas Used
Decay Constant
decay_constant = log(2) / half_life_sActivity
activity_bq = log(2) / half_life_s * num_atomsActivity (Ci)
activity_ci = log(2) / half_life_s * num_atoms / 3.7e10Variables
| Variable | Description | Default |
|---|---|---|
num_atoms | Number of Atoms | 100000000000000000000 |
half_life_s | Half-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).
- 01lambda = ln(2) / t_half = 0.6931 / 3600 = 1.925e-4 /s
- 02A = lambda * N = 1.925e-4 * 1e20
- 03A = 1.925e16 Bq
- 04A = 1.925e16 / 3.7e10 = 520,270 Ci
Frequently Asked Questions
What is a becquerel?
One becquerel (Bq) equals one radioactive decay per second. It is the SI unit of activity, named after Henri Becquerel.
What is a curie?
An older unit of activity: 1 Ci = 3.7 x 10^10 Bq. Originally defined as the activity of 1 gram of radium-226.
Does activity change over time?
Yes. As atoms decay, N decreases, so activity decreases exponentially: A(t) = A_0 * (1/2)^(t/t_half).
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