Question

Question: If a sample is tested for presence of potassium-40 and is found to have undergone 4.5 half lives, what is the age of the object?

Problem set up and info:
Half-life = 1.25 billion years
Number of half-lives passed x years per ½ life = age of sample
4.5 x 1.25 = 5.625 billion years old sample

Answer 1

To calculate the age of the sample that has undergone 4.5 half-lives of potassium-40, you can use the formula you provided:

\[
\text{Age of the sample} = \text{Number of half-lives} \times \text{Years per half-life}
\]

From the problem setup:

- Number of half-lives: 4.5
- Half-life of potassium-40: 1.25 billion years

Now, plug these values into the formula:

\[
\text{Age of the sample} = 4.5 \times 1.25 \text{ billion years}
\]

Calculating this gives:

\[
\text{Age of the sample} = 4.5 \times 1.25 = 5.625 \text{ billion years}
\]

Therefore, the age of the object is **5.625 billion years**.