alleryMean lifetime τ of radioactive nucleus vs half-life T₁/₂:
Aτ = 2 × T₁/₂
Bτ = T₁/₂ × ln 2
Cτ = T₁/₂
Dτ = T₁/₂ / ln 2 ≈ 1.44 × T₁/₂
Answer & Solution
Correct answer: D. τ = T₁/₂ / ln 2 ≈ 1.44 × T₁/₂
τ = 1/λ = T₁/₂ / ln 2 ≈ 1.443 × T₁/₂.
Mean lifetime ≈ 1.44 × half-life.
After τ, N drops to N₀/e ≈ 37%.
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