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In a radioactive material the activity at time t₁ is R₁ and at a later time t₂ it is R₂. If the decay constant of the material is λ, then

1. R₁ = R₂e^(λ(t₂ − t₁))
2. R₁ = R₂e^(t₂ / t₁)
3. R₁ = R₂
4. R₁ = R₂e^(−λ(t₂ − t₁))

Correct answer: R₁ = R₂e^(−λ(t₂ − t₁))

Solution

The activity of a radioactive material decreases exponentially with time, following the relation R = R₀e^(-λt). Rearranging for two different times t₁ and t₂, we get R₁ = R₂e^(-λ(t₂ - t₁)).

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