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 205 grams of a radioactive isotope, how much will be left after 6 half-lives? Use the calculator provided and round your answer to the nearest gram. grams
Ask by Hobbs Harrington. in Mexico
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
After 6 half-lives, 3 grams of the radioactive isotope will remain.
Solution
To determine how much of a radioactive isotope is left after a certain number of half-lives, you use the formula:
Remaining amount = Initial amount × (1/2)^(number of half-lives)
Here, the initial amount is 205 grams and the number of half-lives is 6. Plugging in the numbers:
Remaining amount = 205 × (1/2)^6
Remaining amount = 205 × 1/64
Remaining amount = 205/64
Remaining amount ≈ 3.203125 grams
Rounded to the nearest gram, the final answer is 3 grams.
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Simplify this solution Bonus Knowledge
After the first half-life, you'll have 102.5 grams left, after the second, it’s 51.25 grams, and so on. By the time you reach the 6th half-life, you will have approximately 3.21 grams remaining. Rounding it will give you 3 grams left of the radioactive isotope! Just remember, every time a half-life passes, you're halving what you had! So for any similar calculation, just keep halving your amount for each half-life period you're interested in! It’s a fun little exponential decline dance!
