A radioactive material has half-life 64 months. How long will it take for one eighth of the original material to remain?

Solution & explanation

1. Given: T½ = 64 months; remaining fraction = 1/8.

2. Write the remaining fraction as a power of one half.

   $$\frac{1}{8}={\left(\frac{1}{2}\right)}^3$$

3. Therefore 3 half-lives have elapsed.

4. Multiply by the duration of one half-life.

   $$t=3\times 64=192$$

5. State the result with units: t = 192 months.

192 months