Question

How many milligrams of a 15.0 mg sample of radium-226 remain after 6396 years if the half-life of radium-226 is 1599 years?

Answer 1

`0.9375mg`

Explanation:

`6396/1599 = 4`

the half life of radium-226 is `1599` years, so after `6396` years, `4` half-lives will have passed.

`1` half-life is the time taken for the mass of the sample of radium-226 to halve, or multiply by `1/2`.

`4` half-lives is the time taken for the mass of radium-226 to halve `4` times, or multiply by `(1/2)^4`.

`(1/2)^4 = 1/16`.

this means that after `4` half-lives, `1/16` of the original sample will be left.

`1/16 * 15.0mg = 0.9375mg`