Answer :
Final answer:
It takes approximately 50-60 years for a 15-milligram sample of caesium-137 to decay to 5 milligrams.
Explanation:
The half-life concept in physics corresponds to the time it takes for half the original amount of a radioactive substance to decay. In the case of caesium-137, this period is 30 years. When a radioactive substance decays, its mass decreases by half every half-life period. Therefore, if we start with 15 milligrams of caesium-137, after one half-life (30 years), we will have half of that amount, or 7.5 milligrams, left. It would take another half-life (another 30 years) for the remaining 7.5 milligrams to drop by half, leaving 3.75 milligrams. However, we're aiming for 5 milligrams to remain, which falls between the first and second half-life. It takes less than two full half-lives for the sample to decay to 5 milligrams. Thus, the process takes about 50-60 years, closer to being two complete half-lives, but not quite.
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