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The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 180 grams of a radioactive isotope, how much will be left after 3 half-lives?

Question

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 180 grams of a radioactive isotope, how much will be left after 3 half-lives?

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Solution

To solve this problem, we need to understand that with each half-life, the quantity of the isotope is halved.

  1. After the first half-life, the quantity will be reduced to half of 180 grams, which is 90 grams.

  2. After the second half-life, the quantity will be halved again, leaving 45 grams.

  3. After the third half-life, the quantity will be halved once more, leaving 22.5 grams.

So, after 3 half-lives, there will be 22.5 grams of the radioactive isotope left.

This problem has been solved

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