# 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?

May 24, 2018

$0.9375 m g$

#### Explanation:

$\frac{6396}{1599} = 4$

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 $\frac{1}{2}$.

$4$ half-lives is the time taken for the mass of radium-226 to halve $4$ times, or multiply by ${\left(\frac{1}{2}\right)}^{4}$.

${\left(\frac{1}{2}\right)}^{4} = \frac{1}{16}$.

this means that after $4$ half-lives, $\frac{1}{16}$ of the original sample will be left.

$\frac{1}{16} \cdot 15.0 m g = 0.9375 m g$