# The half-life of Tungsten-181 is 121 days. If you start with 3 pounds of it, how much do you have after 7 years?

May 7, 2018

$\approx 1.32 \times {10}^{-} 6$ pounds

#### Explanation:

Convert the number of years into days so that we can determine how many half-lives have passed.

7 years= $\left(365.25 \times 7\right) = 2556.75$ days

$\frac{2556.75}{121} \approx 21.13$ Half-lives

Use the equation:

$M = {M}_{0} \times {\left(\frac{1}{2}\right)}^{n}$

$n$= number of half-lives

${M}_{0}$= initial mass

$M$=final mass

Hence, as the initial mass is 3 pounds and the number of half-lives is 21.13:

$M = 3 \times {\left(\frac{1}{2}\right)}^{21.13}$

$M \approx 1.32 \times {10}^{-} 6$ pounds remain after 7 years.