# The isotope chromium-51 has a half-life of 28 days. If the original sample had a mass of 28.0 grams, what mass of the chromium-51 sample remains after 84 days?

May 30, 2016

$3.50 g$

#### Explanation:

To find the mass of the chronium-51 sample that remains after $84$ days, we can use the half-life formula.

Recall the half-life formula:

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} A = {A}_{0} {\left(\frac{1}{2}\right)}^{\frac{t}{h}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

where:
$A =$final amount
${A}_{0} =$initial amount
$t =$time elapsed
$h =$time for half of initial amount to remain after decay (also known as half-life)

Plugging in our known values,

$A = 28.0 g {\left(\frac{1}{2}\right)}^{\left(84 \textcolor{w h i t e}{i} \text{days")/(28color(white)(i)"days}\right)}$

$A = \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{3.50 g} \textcolor{w h i t e}{\frac{a}{a}} |}}}$