A sample cerium-141 for a diagnostic test was dissolved in saline solution to an activity of 4.5 millicuries/mL. If the patient undergoing the test needs dose of 10. millicuries, how much of the solution a should be injected into the patient?

Question

Wyatt Atkins · Accepted Answer

#"2.2 mL"#

All you have to do here is to use the known composition of the saline solution as a conversion factor to figure out how many milliliters would contain #10# millicuries.

So, you know that you dissolve your sample of cerium-141 in a saline solution and get an activity of #"4.5 millicuries/mL"#. This tells you that every #"1 mL"# of saline solution will contain enough cerium-141 to account fo an activity of #"4.5 millicuries"#.

Moreover, you know that solutions are homogeneous mixtures, which implies that they have the same composition throughout.

This means that an activity of #"10. millicuries"# will correspond to a volume of

#10. color(red)(cancel(color(black)("millicuries"))) * "1 mL saline"/(4.5color(red)(cancel(color(black)("millicuries")))) = color(darkgreen)(ul(color(black)("2.2 mL saline")))#

The answer is rounded to two sig figs.

Xavier Avery · Answer

undefined The patient should be injected with 2.22 mL of the solution.