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

Feb 28, 2016

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

#### Explanation:

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

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

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

$3 \cdot 30.17 \approx 90.5$

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