At the end of 14 min, 1/16 of a sample of radioactive Polonium remains. The corresponding half-life is:
Correct answer: D. (7/2) min
- A. (7/8) min
- B. (8/7) min
- C. (7/4) min
- D. (7/2) min
Explanation
N(t) = No × (1/2)^(t/T)N(t) = remaining amount after time tNo = initial amountt = time elapsed (14 min)T = half-life (unknown)Given:N(t) = 1/16 N0 (remaining amount after 14 min)(1/16) = (1/2)^(14/T)(1/2)^4 = (1/2)^(14/T)Comparing the exponents, we get:4 = 14/TSolving for T, we get:T = 14/4T = 7/2T = 3.5 min
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