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 6 half-lives?
Use the calculator provided and round your answer to the nearest gram.

Answer 1

To determine how much of a radioactive isotope remains after 6 half-lives, we can use the formula:

\[
\text{Remaining Amount} = \text{Initial Amount} \times \left( \frac{1}{2} \right)^n
\]

Where:
- \(\text{Initial Amount} = 145 \text{ grams}\)
- \(n = 6\) (the number of half-lives)

Now we can calculate:

\[
\text{Remaining Amount} = 145 \times \left( \frac{1}{2} \right)^6
\]

\[
\left( \frac{1}{2} \right)^6 = \frac{1}{64}
\]

So,

\[
\text{Remaining Amount} = 145 \times \frac{1}{64}
\]

Calculating this gives:

\[
\text{Remaining Amount} = \frac{145}{64} \approx 2.265625
\]

Rounding to the nearest gram, we get:

\[
\text{Remaining Amount} \approx 2 \text{ grams}
\]

Thus, after 6 half-lives, approximately **2 grams** of the radioactive isotope will remain.