The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will rem

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Question

The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be

Accepted Answer

Correct Answer: C — 1/(2√2)Step-by-step Solution:The fraction of activity remaining after time t is given by:A/A₀ = (1/2)^(t/T₁/₂) = (1/2)^(150/100) = (1/2)^(3/2).(1/2)^(3/2) = 1 / 2^(3/2) = 1 / (2 × √2) = 1/(2√2).Why other options are incorrect: Option B (1/2) corresponds to exactly one half-life, i.e., t = 100 hours. Option A (2/3√2) and D (2/3) do not arise from the correct decay law.Key Concept: Radioactive decay: A = A₀ (1/2)^(t/T₁/₂). Activity is proportional to the number of undecayed nuclei, so the fraction of activity remaining equals the fraction of nuclei remaining.

The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be

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The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be

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