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Radioactive decay is the spontaneous transformation of unstable atomic nuclei over time. The half-life is the time for half the atoms to decay; after n half-lives, N₀/2ⁿ atoms remain.

Formula

N(t) = N₀ × e^(−λt) | t½ = ln(2)/λ | N(t) = N₀ × (½)^(t/t½)

N(t): Remaining nuclei at time t
N₀: Initial number of nuclei
λ: Decay constant (s⁻¹)
t: Time elapsed (s)
t½: Half-life (s or years)

Guida passo passo

1N(t) = N₀ × (½)^(t/t½)
2Decay constant λ = ln(2)/t½
3After 1 half-life: 50% remains; 2: 25%; 3: 12.5%
4Used in carbon dating, nuclear medicine, and waste management

Esempi risolti

Ingresso

Carbon-14, t½=5,730yr, elapsed 11,460yr (2 half-lives)

Risultato

N = N₀ × 0.25 = 25% of original carbon-14 remains

Domande frequenti

What is Radioactive Decay?

Radioactive decay is the spontaneous transformation of unstable atomic nuclei over time. The half-life is the time for half the atoms to decay; after n half-lives, N₀/2ⁿ atoms remain

How accurate is the Radioactive Decay calculator?

The calculator uses the standard published formula for radioactive decay. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.

What units does the Radioactive Decay calculator use?

This calculator works with inches, percentages. You can enter values in the units shown — the calculator handles all conversions internally.

What formula does the Radioactive Decay calculator use?

The core formula is: N(t) = N₀ × (½)^(t/t½). Each step in the calculation is shown so you can verify the result manually.

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