Suppose 62.0% of a sample of radioactive polonium-218 remains after 2.14 minutes.Estimate the half-life of Po-218.

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Quizplus · Accepted Answer

The half-life of a radioactive substance is the time it takes for half of the substance to decay. In this case, 62.0% of the substance remains after 2.14 minutes, which means that 38.0% of the substance has decayed. The half-life can be calculated using the formula:t1/2 = (ln 2) / kwhere t1/2 is the half-life, ln is the natural logarithm, and k is the decay constant. The decay constant can be calculated using the formula:k = (ln 2) / t1/2Substituting the given values into the formula, we get:k = (ln 2) / 2.14 minutes = 0.323 minutes^-1Substituting this value into the formula for the half-life, we get:t1/2 = (ln 2) / 0.323 minutes^-1 = 3.10 minutesTherefore, the half-life of Po-218 is 3.10 minutes.