# Mercury-197 is used for kidney scans and has a half-life of 3 days. If the 32 grams of mercury-197 is ordered, but takes 15 days to arrive, how much would arrive in the shipment?

Feb 5, 2017

In 15 days you will have $15 \div 3 = 5$ halvings.
So from the original sample only ${\left(\frac{1}{2}\right)}^{5}$ will be left.
This is $\frac{32}{2} ^ 5 = \frac{32}{32} = 1 g$ effectively.
Of course the shipment will not have shrunk to $1 g$, but it will be 'contaminated' by the decay products of $H g \text{-} 197$