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

1 Answer
Apr 3, 2015

The half-life of your radioisotope is #"6.6 days"#.

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

#"1 half-life" -> 1/2 " left undecayed"#

#"2 half-lives" -> 1/4 " left undecayed"#

#"3 half-lives" -> 1/8 " left undecayed"#

#"4 half-lives" -> 1/16 " left undecayed"#

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

#t/t_("1/2") = 4#

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

#"26.4"/t_("1/2") = 4 => t_("1.2") = 26.4/4 = "6.6 days"#