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A half-life calculator computes how much of a radioactive substance, drug, or any exponentially decaying quantity remains after a given number of half-lives.
Fórmula
Remaining = Initial × (0.5)^(time / half_life); Time = half_life × log(remaining/initial) / log(0.5)
- N
- Remaining amount (original units)
- N₀
- Initial amount (original units)
- t½
- Half-life (time period)
Guia passo a passo
- 1N(t) = N₀ × (½)^(t/t½)
- 2After n half-lives: N = N₀ / 2ⁿ
- 3Decay constant: λ = ln(2)/t½ ≈ 0.693/t½
- 4Mean lifetime: τ = 1/λ = t½/ln(2) ≈ 1.443 × t½
Exemplos resolvidos
Entrada
100g substance, half-life 10 years, after 40 years
Resultado
4 half-lives; N = 100/2⁴ = 6.25g remaining
Perguntas frequentes
What does half-life mean?
Time for substance to decay to half its original amount. After 2 half-lives, 25% remains. After 3, 12.5%.
Is carbon-14 dating accurate?
Accurate for organic material 300-50,000 years old. Beyond that, uncertainty increases. Half-life: 5,730 years.
Do all atoms decay the same rate?
Within a sample, decay is random—but statistically predictable. Half-life is constant for each isotope.
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