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A radioactive sample of substance A has an activity of 10 mCi, where 1 Ci = 3.7 × 10¹⁰ decays per second. It contains twice as many nuclei as a separate sample of radioactive substance B, whose activity is 20 mCi. Which pair of half-lives for A and B is correct, respectively?
- 5 days and 10 days
- 10 days and 40 days
- 20 days and 5 days
- 20 days and 10 days
Correct answer: 20 days and 5 days
Solution
Activity R = lambda*N. R_A = lambda_A*N_A = 10 and N_A = 2*N_B, so lambda_A*N_B = 5. R_B = lambda_B*N_B = 20. Thus lambda_B/lambda_A = 20/5 = 4, and since T is inversely proportional to lambda, T_A = 4*T_B. Only 20 days and 5 days satisfies this.
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