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?

1 Answer
Dec 28, 2015

Answer:

#"% 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."