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Calculate remaining amount, half-life period, or elapsed time for exponential decay. Includes decay table showing quantity over multiple half-life periods.
Half-life is the time required for a quantity undergoing exponential decay to decrease to half of its initial value, commonly used in nuclear physics, pharmacology, and chemistry.
Remaining Amount
125
| Half-Lives | Time | Remaining | % |
|---|---|---|---|
| 0 | 0 | 1000 | 100.00% |
| 1 | 5 | 500 | 50.00% |
| 2 | 10 | 250 | 25.00% |
| 3 | 15 | 125 | 12.50% |
| 4 | 20 | 62.5 | 6.25% |
| 5 | 25 | 31.25 | 3.13% |
| 6 | 30 | 15.625 | 1.56% |
| 7 | 35 | 7.8125 | 0.78% |
Formula
N(t) = N₀ × (½)^(t / t½)N(t) = Amount remaining after time t
N₀ = Initial amount
t = Elapsed time
t½ = Half-life period
Worked Example
1000g substance with 5-year half-life after 15 years
Did you know? Bismuth-209, once thought to be the heaviest stable isotope, was found in 2003 to be radioactive with a half-life of 1.9 × 10¹⁹ years — over a billion times the age of the universe (source: Nature, 2003).
Sources
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