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Answer :
Final answer:
Approximately 90 years are required for 24 mg of cesium-137 to decay to 1.5 mg, using the half-life of cesium-137 which is about 30 years.
Explanation:
The question asks how many years are required for 24 mg of cesium-137 to decay to 1.5 mg. To find the time required for this decay, we use the concept of half-life. The half-life of cesium-137 is about 30 years. During each half-life, the quantity of the substance is reduced by half.
To solve this problem, we need to determine how many half-lives it takes for 24 mg to decay to 1.5 mg. This can be calculated using the formula:
N = N0 (1/2)^(t/T)
Where N is the final amount, N0 is the initial amount, t is the time elapsed, and T is the half-life. By rearranging this formula and solving for t, we can determine the elapsed time in years. Applying this formula and the known half-life for cesium-137, we can calculate that approximately 90 years are required for 24 mg of cesium-137 to decay to 1.5 mg.
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