# What is the half-life of a radioisotope if 1/16 of it remains undecayed after 26.4 days?

##### 1 Answer

The half-life of your radioisotope is

When numbers allow it, the quickest way to determine the half-life of a radioisotope is to use the fraction left undecayed as a measure of how many half-lives have passed.

You know that the mass of a radioactive isotope gets **halved** with the passing of *every* half-life, which means that

As you can see, **4** half-lives must pass until you have **1/16** of the original sample. Mathematically, this means that

Since you know that **26.4 days** have passed, the isotope's half-life will be