Questions: 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 3 half-lives? Use the calculator provided and round your answer to the nearest gram. grams

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 3 half-lives? Use the calculator provided and round your answer to the nearest gram. grams
Transcript text: 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 3 half-lives? Use the calculator provided and round your answer to the nearest gram. $\square$ grams
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Solution

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Solution Steps

Step 1: Determine the Initial Mass

The initial mass of the radioactive isotope is given as 210 grams.

Step 2: Understand the Concept of Half-Life

Each half-life reduces the quantity of the isotope to half of its previous amount.

Step 3: Calculate the Remaining Mass After Each Half-Life
  • After 1 half-life: \( \frac{210}{2} = 105 \) grams
  • After 2 half-lives: \( \frac{105}{2} = 52.5 \) grams
  • After 3 half-lives: \( \frac{52.5}{2} = 26.25 \) grams
Step 4: Round to the Nearest Gram

Round 26.25 grams to the nearest whole number, which is 26 grams.

Step 5: Final Answer

The amount of the radioactive isotope left after 3 half-lives is 26 grams.

Final Answer

\(\boxed{26}\) grams

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