A certain isotope has a half-life of 14.7 min.How long will it take for 24.2% of the isotope to decay?

Question

Quizplus · Accepted Answer

The time it takes for 24.2% of the isotope to decay can be found using the half-life formula, but a simpler approach is to recognize that in one half-life (14.7 minutes), 50% of the isotope remains. To decay to 24.2%, it's less than one half-life. The question, however, seems to ask for the time to decay to 24.2%, but the answer given (5.88 min) doesn't directly correspond to this calculation based on typical half-life decay formulas. It appears there might be a misunderstanding in the question or answer interpretation. Normally, to find the time for a specific percentage to decay, you'd use the formula involving the natural logarithm and the decay constant, but none of the provided options directly match the expected calculation for 24.2% decay. The closest standard approach would suggest looking at how much time it takes to reach a certain remaining percentage, not just the decayed portion. However, without the exact formula application provided in the options, the answer hints at a possible calculation mistake or a misinterpretation of the decay process.

A Certain Isotope Has a Half-Life of 14