# If 100.0 g of a radioactive isotope that has a half life of 25 years, identify the amount of that isotope that will remain after 100 years?

May 17, 2014

The amount remaining will be 6.2 g.

The number of half-lives is n = t/t_½

For each half-life, you divide the total amount of the isotope by 2, so

Amount remaining = $\frac{\text{original amount}}{2} ^ n$ or

$A = {A}_{0} / {2}^{n}$

n = t/t_½ = (100" yr")/(25" yr") = 4.0 half-lives

$A = {A}_{0} / {2}^{n} = \frac{100.0 \text{ g")/2^4.0 = (100.0" g}}{16}$ = 6.2 g