If a radioactive element has a half-life of 40 minutes. The initial count rate was 1000 per minute, then how long will it take for the count rate to drop to 125 per minutes?
Correct answer: A. 120 minutes
- A. 120 minutes
- B. 90 minutes
- C. 30 minutes
- D. 60 minutes
Explanation
N(t) = N0 * (1/2)^(t / T),In this case, N(t) is 125 per minute, No is 1000 per minute, and T is 40 minutes. We need to solve for t, the time it takes for the count rate to drop to 125.125 = 1000 * (1/2)^(t / 40)(1/2)^(t / 40) = 125 / 1000(1/2)^(t / 40) = 1/8ln((1/2)^(t / 40)) = ln(1/8)Using the properties of logarithms, you can bring down the exponent:(t / 40) * ln(1/2) = ln(1/8)t / 40 = ln(1/8) / ln(1/2)t / 40 = 3t = 3 * 40 = 120 minutes.So, it will take 120 minutes for the count rate to drop to 125 per minute.
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About Half-life and Rate of Decay
Half-life is the time required for half the unstable nuclei in a sample to decay, and it remains constant for a particular radioactive nuclide. Questions use the exponential decay law, decay constant, activity, remaining quantity and mean life. Radioactive decay is random for individual nuclei but predictable for large samples.
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