Radioactive Decay (Advanced) Calculator Formula
Understand the math behind the radioactive decay (advanced) calculator. Each variable explained with a worked example.
Formulas Used
Remaining Activity
remaining = initial_activity * exp(-lambda * elapsed_time)Fraction Remaining
fraction = exp(-lambda * elapsed_time) * 100Fraction Decayed
decayed_pct = (1 - exp(-lambda * elapsed_time)) * 100Half-Lives Elapsed
half_lives_elapsed = half_livesVariables
| Variable | Description | Default |
|---|---|---|
initial_activity | Initial Activity (A0)(Bq) | 1000000 |
half_life | Half-Life(days) | 8 |
elapsed_time | Elapsed Time(days) | 24 |
lambda | Derived value= log(2) / half_life | calculated |
half_lives | Derived value= elapsed_time / half_life | calculated |
How It Works
Radioactive Decay Law
Radioactive decay follows first-order kinetics. The activity (and number of atoms) decreases exponentially with time.
Formula
A(t) = A0 × e^(-lambda × t) = A0 × (1/2)^(t/t½)
where lambda = ln(2)/t½ is the decay constant. After one half-life, 50% remains. After two, 25%. After ten, only 0.098% remains.
Worked Example
I-131 (t½ = 8 days) with initial activity 1 MBq after 24 days.
initial_activity = 1000000half_life = 8elapsed_time = 24
- 01Half-lives elapsed = 24 / 8 = 3.0
- 02Fraction remaining = (1/2)³ = 0.125 = 12.5%
- 03A(24) = 1,000,000 × 0.125 = 125,000 Bq
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