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The activity of a radioactive sample is measured as 9750 counts per minute at t = 0 and as 975 counts per minute at t = 5 minutes. The decay constant is approximately

1. 0.922 per minute
2. 0.691 per minute
3. 0.461 per minute
4. 0.230 per minute

Correct answer: 0.691 per minute

Solution

The decay constant can be calculated using the formula for radioactive decay: \( A = A_0 e^{-\lambda t} \). Taking the natural logarithm of both sides and solving for \( \lambda \), we get \( \lambda = \frac{1}{t} \ln \frac{A_0}{A} \). Substituting \( A_0 = 9750 \), \( A = 975 \), and \( t = 5 \) minutes, \( \lambda \approx 0.691 \) per minute.

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