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Answer :
Final answer:
It would take more than 180 years for the amount of cesium-137 to decay to less than 1, with each 30-year half-life reducing the amount by half. None of the options (a, b, c, d) provided in the question are correct.
Explanation:
The question relates to the concept of radioactive decay and half-life. To determine the time it takes for cesium-137, which has a half-life of 30 years, to decay from an initial amount of 100 units to less than 1 unit, you can use the iterative process of halving the quantity through each half-life period.
After 30 years (one half-life), you would have 50 units remaining.
After 60 years (two half-lives), you would have 25 units remaining.
After 90 years (three half-lives), you would have 12.5 units remaining.
After 120 years (four half-lives), you would have 6.25 units remaining.
After 150 years (five half-lives), you would have 3.125 units remaining.
After 180 years (six half-lives), you would have 1.5625 units remaining.
Following this pattern, it becomes evident that it will take slightly more than 180 years for the amount of cesium-137 to be less than 1. Thus, none of the provided options (a, b, c, d) are correct.
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