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 165 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.

To solve this problem, we need to understand the concept of half-life. Each half-life reduces the quantity of a radioactive isotope to half of its previous amount.

Given:
- Initial mass, \( M_0 = 165 \) grams
- Number of half-lives, \( n = 6 \)

The formula for the remaining mass after \( n \) half-lives is:

\[
M = M_0 \times \left(\frac{1}{2}\right)^n
\]

where:
- \( M \) is the remaining mass,
- \( M_0 \) is the initial mass,
- \( n \) is the number of half-lives.

Plugging in the given values:

\[
M = 165 \times \left(\frac{1}{2}\right)^6
\]

Let's calculate the remaining mass step-by-step.After 6 half-lives, there will be **3 grams** of the radioactive isotope remaining.

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

Here are 5 related questions that might interest you:
1. What would the remaining mass be after 10 half-lives?
2. How is the half-life formula derived mathematically?
3. If the half-life of a substance is 5 years, how much will remain after 15 years?
4. What is the general formula for exponential decay?
5. How can we calculate the half-life if we know the initial and final quantities and time?

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

Learn how to calculate the remaining mass of a radioactive isotope after 6 half-lives. Starting with 165 grams of the isotope, understand the concept of exponential decay and apply the half-life formula. Suitable for students in Grades 9-12.

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