Question

How much of a 1.00 mg sample of iodine remains after 3 half-lives?

Answer 1

0.125 mg.

Step-by-step explanation

The mass of a radioactive species decrease by
`(1)/(2)` by the end of each half-life.

For this 1.00 mg sample of unknown half-life:

Mass of the sample at the end of the n-th half-life;

`\begin{array}{ll} \text{n} & \text{Mass} \; (\text{mg})\\1 & 1.00 * (1)/(2) = 0.500\\2 & 1.00 * {(1)/(2)}^(2) = 0.250 \\3 & 1.00 * {(1)/(2)}^(3) = 0.125\\\dots & \dots \end{array}`.

As a result,

`1.00 * {(1)/(2)}^(3) = 0.125 \; \text{mg}`

of the sample remains after three half-lives.