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 210 grams of a radioactive isotope, how much will be left after 4 half-lives?

Answer 1

After 4 half-lives of a radioactive isotope starting at 210 grams, 13.125 grams would remain due to the process of radioactive decay.

Step-by-step explanation:

The question is asking how much of a radioactive isotope will remain after it goes through 4 half-lives. Starting with 210 grams, after one half-life there will be half of that amount, so 105 grams. Following the concept of radioactive decay, we can continue this halving for each subsequent half-life:

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• After 1 half-life: 210g / 2 = 105g
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• After 2 half-lives: 105g / 2 = 52.5g
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• After 3 half-lives: 52.5g / 2 = 26.25g
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• After 4 half-lives: 26.25g / 2 = 13.125g

Therefore, after 4 half-lives, you would be left with 13.125 grams of the radioactive isotope.