Question

if a radioactive isotope has a half-life of 30 minutes, and you determine that 12.5% of the original concentration of that isotope is left within a sample, how old is the sample?

Answer 1

The age of a sample with 12.5% of a radioactive isotope remaining, which has a half-life of 30 minutes, would be 90 minutes, as this represents three half-lives (3 * 30 minutes).

Step-by-step explanation:

If a radioactive isotope has a half-life of 30 minutes and we determine that 12.5% of the original concentration of the isotope is left within a sample, we can calculate the age of the sample. The key is to understand that with each half-life, the amount of remaining isotope will be halved. After one half-life, 50% remains, after two half-lives, this is reduced to 25%, and after three half-lives, only 12.5% would remain.

Since 12.5% is the amount remaining after three half-lives, we can calculate the total time by multiplying the number of half-lives by the length of one half-life. Hence, the calculation would be:

3 half-lives * 30 minutes per half-life = 90 minutes

Thus, the sample would be 90 minutes old.