# The half life of a radioactive isotope is 350 years. How do you find the amount remaining after 800 years, if the initial amount is 64 grams?

Nov 29, 2016

The amount remaining $= 13.13 g$

#### Explanation:

Use the equation

$N \left(t\right) = {N}_{0} {e}^{- \lambda t}$

${N}_{0} =$initial amount $= 64 g$

The half life is $= {t}_{\frac{1}{2}} = \ln \frac{2}{\lambda}$

${t}_{\frac{1}{2}} = 350 y$

Therefore, $\lambda = \ln \frac{2}{350} {y}^{- 1}$

$t = 800 y$

$N \left(t\right) = 64 \cdot {e}^{\left(- \ln \frac{2}{350}\right) \cdot 800}$

$= 13.13 g$