If a 100.0 gram sample of a radioactive isotope goes through three half-lives, how much of the original radioactive isotope will remain?
2^3 = 8
So 1/8 of the sample will remain.
1/8 x 100 = 12.5g remaining.
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To determine how much of the original radioactive isotope remains after three half-lives, we need to understand the concept of half-life.
The half-life of a radioactive isotope is the time it takes for half of the initial quantity of the isotope to decay. After each half-life, half of the remaining isotope will decay, leaving only half of the previous amount.
In this case, we can calculate the amount remaining after each half-life:
Half-life 1: After the first half-life, half of the original sample will remain. So, 100.0 grams / 2 = 50.0 grams.
Half-life 2: After the second half-life, half of the remaining sample from the previous step will remain. So, 50.0 grams / 2 = 25.0 grams.
Half-life 3: After the third half-life, half of the remaining sample from the previous step will remain. So, 25.0 grams / 2 = 12.5 grams.
Therefore, after three half-lives, 12.5 grams of the original radioactive isotope will remain.