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The question is asking for the remaining quantity of a radioactive isotope after 5 half-lives, starting with an initial amount of 120 grams.

### Solution:
The amount of a substance left after a certain number of half-lives can be found using the formula:
\[
A = A_0 \times \left( \frac{1}{2} \right)^n
\]
where:
- \( A \) is the remaining amount,
- \( A_0 \) is the initial amount (120 grams in this case),
- \( n \) is the number of half-lives (5 in this case).

#### Step-by-Step Calculation:
1. Substitute the values into the formula:
   \[
   A = 120 \times \left( \frac{1}{2} \right)^5
   \]
2. Calculate \( \left( \frac{1}{2} \right)^5 \):
   \[
   \left( \frac{1}{2} \right)^5 = \frac{1}{32} = 0.03125
   \]
3. Multiply by the initial amount:
   \[
   A = 120 \times 0.03125 = 3.75
   \]

Rounding to the nearest gram, the remaining amount after 5 half-lives is **4 grams**.

Would you like more details on this calculation or have any questions?

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Here are 5 additional questions to expand on this topic:

1. What is the remaining mass after 3 half-lives if starting with 100 grams?
2. How does the half-life of an isotope relate to its decay rate?
3. If the initial mass was 200 grams, how much would be left after 6 half-lives?
4. How can you determine the number of half-lives passed if you know the initial and remaining masses?
5. What real-world applications use half-life calculations?

**Tip:** When dealing with half-life problems, remember that each half-life reduces the remaining quantity by half, regardless of the initial amount.

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 120 grams of a radioactive isotope, how much will be left after 5 half-lives?

Learn how to calculate the remaining mass of a radioactive isotope with an initial amount of 120 grams after 5 half-lives using the exponential decay formula. Perfect for students in Grades 9-12.

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