Radioactive isotopes can sometimes emit 
or 
radiation, which can be very dangerous to people. However, they can be very useful for medical purposes, so long as the proper quantity is used. If the safety standard for a radioactive injection of phosphorus requires that less than 0.01g remains in the body after 90 days after the injection, what is the maximum initial dose? The half-life of phosphorous is 14.29 days.
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Correct Answer: B. Lead (Pb).
Nt is given as 0.01g, and we want to calculate N0. The decay constant can be found using:
and find that it is 0.0484 days. The total time is 90 days, and the number of mols of phosphorus is 0.1/32, since phosphorus has a molecular weight of 32. Using:
which is the half life expectancy equation, we find that the maximum injection amount is 0.78g.
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