A radioactive substance has half-life 20 min. Let t₁ be the time when 1/3 of the sample has decayed and t₂ the time when 2/3 has decayed. Find the approximate interval t₂ - t₁.
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Question

A radioactive substance has half-life 20 min. Let t₁ be the time when 1/3 of the sample has decayed and t₂ the time when 2/3 has decayed. Find the approximate interval t₂ − t₁.

G1 Physics · Accepted Answer

At t₁, 1/3 has decayed, so 2/3 remains. At t₂, 2/3 has decayed, so 1/3 remains. Thus N(t₂)/N(t₁) = (1/3)/(2/3) = 1/2. A drop by a factor 2 takes one half-life, so t₂−t₁ = 20 min. Correct answer: A.