The activity of a radioactive sample is measured at two instants separated by 10 h. The first activity is exactly 9 times the second activity. The half-life is closest to:
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Question

The activity of a radioactive sample is measured at two instants separated by 10 h. The first activity is exactly 9 times the second activity. The half-life is closest to:

G1 Physics · Accepted Answer

Radioactive activity obeys A(t) = A₀ exp(−λt). Given the activity decreases by a factor 9 in 10 h: A₁ ÷ A₂ = 9 = exp(λ×10). Therefore, λ = ln9 ÷ 10. Half-life is T₁⁄₂ = ln2 ÷ λ = 10ln2 ÷ ln9. Using ln2 ≈ 0.693 and ln9 ≈ 2.197: T₁⁄₂ ≈ 10×0.693 ÷ 2.197 ≈ 3.15 h. Correct option: B.