Question

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?

Answer 1

`"% Amount remaining after 67 months" = 15.3%" to 3 significant figures"`

Explanation:

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

`67" months" = 5.58334" years"`

`"Amount remaining" = "Beginning Amount"/2^n`

Where:

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

`:. "% Amount remaining after 67 months" = 100/(2^((5.58334/2.062)))`

`= 15.30706554%`

`= 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."