A radioactive material is reduced to 1/8 of its original amount in 3 days. If 8 × 10⁻³ kg of the material is left after 5 days, the initial amount of the material is:
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Question

A radioactive material is reduced to 1/8 of its original amount in 3 days. If 8 × 10⁻³ kg of the material is left after 5 days, the initial amount of the material is:

G1 Physics · Accepted Answer

The radioactive material becomes 1/8 of its original amount in 3 days. Since 1/8 = (1/2)³, three half-lives occur in 3 days. Therefore half-life = 1 day. After 5 days, the remaining fraction is (1/2)⁵ = 1/32 Given remaining mass: m = 8×10⁻³ kg = 8 g Initial mass: m₀ = 32×8 g = 256 g Hence option D follows.