Answer :

After 6 minutes (360 seconds), approximately \(0.000260754\) or \(2.60754 \times 10^{-4}\) fraction of a sample of Cs-124 will remain, due to its half-life of 31 seconds.

  • The half-life of a radioactive substance is the time it takes for half of a sample to decay. In this case, Cesium-124 (Cs-124) has a half-life of 31 seconds.
  • To find the fraction of a sample that remains after a certain time, we can use the formula: \[ \text{Remaining fraction} = \left( \frac{1}{2} \right)^{\frac{\text{time elapsed}}{\text{half-life}}} \]
  • Given that 6 minutes is equivalent to \(6 \times 60 = 360\) seconds, we can plug in the values: \[ \text{Remaining fraction} = \left( \frac{1}{2} \right)^{\frac{360}{31}} \approx 0.000260754 \]
  • So, after 6 minutes, approximately \(0.000260754\) or \(2.60754 \times 10^{-4}\) fraction of a sample of Cs-124 will remain. This is a very small fraction, indicating that a significant portion of the original sample will have decayed during this time.
  • It's important to note that radioactive decay is an exponential process, and the remaining fraction decreases rapidly as time progresses due to the halving behavior associated with half-lives.

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