Suppose the half life of element K is 20 minutes. If you have 200 g sample of K, how much of element K will be left after 60 minutes?

Mar 31, 2016

$25 \textcolor{w h i t e}{i} g$

Explanation:

Recall that the formula for half-life is:

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} y = a {\left(b\right)}^{\frac{t}{h}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

where:
$y =$final amount
$a =$inital amount
$b =$growth/decay
$t =$time elapsed
$h =$half-life

To find the amount of the sample left after $60$ minutes, substitute your known values into the equation.

$y = 200 {\left(\frac{1}{2}\right)}^{\frac{60}{20}}$

Solve for $y$.

$y = 200 {\left(\frac{1}{2}\right)}^{3}$

$y = 200 \left(\frac{1}{8}\right)$

$\textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} y = 25 \textcolor{w h i t e}{i} g \textcolor{w h i t e}{\frac{a}{a}} |}}}$