Question

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?

Answer 1

`"2.2 mL"`

Explanation:

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.