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 145 grams of a radioactive isotope, how much will be left after 3 half-lives?

Use the calculator provided and round your answer to the nearest gram.

Answer 1

23 grams

Explanation:

If the half-life of the isotope is the time it takes for the quantity of the isotope to be reduced to half its initial mass, then after one half-life, there will be half the initial amount remains. After two half-lives, there will be one-quarter of the initial amount remaining, and after three half-lives, there will be one-eighth of the initial amount remaining.

So, after three half-lives, the amount remaining will be:

(1/2) x (1/2) x (1/2) x 145 grams ≈ 22.81 grams

Rounding to the nearest gram, the answer is 23 grams. So after three half-lives, there will be approximately 23 grams of the radioactive isotope remaining.