Question

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

Answer 1

`"12.5 g"`

Explanation:

Nuclear half-life, `t_"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):

`"200 g" /2 = "100 g"` decays and `"100 g"` are left.

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

`"100 g" /2 = "50 g"` decays and `"50 g"` are left.

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

`"50 g" /2 = "25 g"` decays and `"25 g"` are left.

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

`"25 g"/2 = "12.5 g"` decays and `"12.5 g"` are left.

So after four half-lives or `32` years, `"12.5 g"` of iodine-131 will be left.