# Radioactive iodine-131 has a half-life of eight days. The amount of a 200.0 gram sample left after 32 days would be?

Jul 3, 2014

$\text{12.5 g}$

#### Explanation:

Nuclear half-life, ${t}_{\text{1/2}}$, is the amount of time required for a quantity of a radioactive material to fall to half its value as measured at the beginning of the time period. In this question, the half-life of iodine-131 is $8$ days, which means that after $8$ days, half of the sample would have decayed and half would be left undecayed.

• after $8$ days (the first half-life):

$\text{200 g" /2 = "100 g}$ decays and $\text{100 g}$ are left.

• after another  days (two half-lives or 16 years):

$\text{100 g" /2 = "50 g}$ decays and $\text{50 g}$ are left.

• after another $8$ days (three half-lives or $24$ years):

$\text{50 g" /2 = "25 g}$ decays and $\text{25 g}$ are left.

• after another $8$ days (four half-lives or $32$ years):

$\text{25 g"/2 = "12.5 g}$ decays and $\text{12.5 g}$ are left.

So after four half-lives or $32$ years, $\text{12.5 g}$ of iodine-131 will be left.