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Answer :
Final answer:
It would take approximately 149.01 years for 24 mg of cesium-137 to decay to 1.5 mg.
Explanation:
To calculate the time required for cesium-137 to decay from 24 mg to 1.5 mg, we can use the concept of half-life. The half-life of cesium-137 is 30.17 years. This means that in every 30.17 years, the amount of cesium-137 will be reduced by half.
We can use the formula:
Final amount = Initial amount * (1/2)^(Number of half-lives)
Let's plug in the values:
1.5 mg = 24 mg * (1/2)^(Number of half-lives)
Solving for the number of half-lives:
(1/2)^(Number of half-lives) = 1.5/24
Taking the logarithm:
Number of half-lives = log(1.5/24) / log(1/2)
Using a calculator:
Number of half-lives = 4.95
Therefore, it would take approximately 4.95 * 30.17 years = 149.01 years for 24 mg of cesium-137 to decay to 1.5 mg.
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