# The half-life of the decay of radioactive cesium(134) has been reported to be 2.062 years. What fraction of the original radioactivity will remain after 67 months?

Dec 28, 2015

$\text{% Amount remaining after 67 months" = 15.3%" to 3 significant figures}$

#### Explanation:

http://www.1728.org/halflife.htm

$67 \text{ months" = 5.58334" years}$

$\frac{\text{Amount remaining" = "Beginning Amount}}{2} ^ n$

Where:

1. $\text{Beginning Amount}$ is the whole sample (here, 100%)
2. $n = \text{elapsed time"/"half-life}$

$\therefore \text{% Amount remaining after 67 months} = \frac{100}{{2}^{\left(\frac{5.58334}{2.062}\right)}}$

= 15.30706554%

$= \frac{30614131}{200000000}$

OR, more simply:

= 15.3%" to 3 significant figures"

As a final note, "original radioactivity" probably isn't the most accurate wording, since radioactivity is a property and would suggest that a single atom of cesium-134 would change how likely it is to decay over time. A better choice of words would be "original sample of radioactive cesium-134."