Question 17.4: How long does it take for a 1.80-mol sample of Th-228 (which......
How long does it take for a 1.80-mol sample of Th-228 (which has a half-life of 1.9 years) to decay to 0.225 mol?
Step-by-Step
Draw a table showing the amount of Th-228 as a function of number of halflives. For each half-life, divide the amount of Th-228 by 2.
\begin{array}{lll} \hline \text{Amount of }Th-228 & \text{Number of Half-Lives} & \text{Time (yrs)} \\ \hline 1.80 \mathrm{~mol} & 0 & 0 \\ 0.900 \mathrm{~mol} & 1 & 1.9 \\ 0.450 \mathrm{~mol} & 2 & 3.8 \\ 0.225 \mathrm{~mol} & 3 & 5.7 \end{array}
It takes three half-lives or 5.7 years for the sample to decay to 0.225 \mathrm{~mol}.
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