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