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?

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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?

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Answer 1 · 2015-12-28T14:53:06

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

Explanation:

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

$67 months = 5.58334 years$ $67" months" = 5.58334" years"$

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

Where:

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

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

$= 15.30706554%$

$= 30614131/200000000$

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."

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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

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