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How many years are required for 28 mg of cesium-137 to decay to 3.5 mg of cesium-137?

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George C. · mrpauller.weebly.com

Feb 28, 2016

$28 m g$ $28 mg$ of cesium-137 will decay to $3.5 m g$ $3.5 mg$ of cesium-137 in $90.5$ $90.5$ years (3 times the half life)

Explanation:

The half life of cesium-137 is approximately $30.17$ $30.17$ years ( $\pm 0.03$ $+-0.03$ )

${log}_{2} (\frac{28}{3.5}) = {log}_{2} (8) = {log}_{2} (2^{3}) = 3$ $log_2 (28/3.5) = log_2 (8) = log_2 (2^3) = 3$

So it will take $3$ $3$ times the half life for the sample to decay from $28 m g$ $28mg$ to $3.5 m g$ $3.5mg$ (one eighth).

$3 \cdot 30.17 \approx 90.5$ $3 * 30.17 ~~ 90.5$

This video shows a sample of Cs-137 being tested by a hand-held detector.

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