A radioactive isotope in a 9.0 mL vial has an intensity of 300. mCi. How much of the liquid should be injected into a patient to deliver a dose of 50. mCi?

Question

Quizplus · Accepted Answer

We can use the formula:
dose = intensity x volume
Rearranging, we get:
volume = dose / intensity

Substituting the given values, we get:
volume = 50. mCi / 300. mCi/mL
volume = 0.1667 mL

However, the question asks for the amount of liquid to be injected, not the volume of the radioactive isotope. Therefore, we need to convert the volume of the isotope to the amount of liquid that needs to be injected.

Since the isotope is in a 9.0 mL vial, we can assume that the entire 0.1667 mL of isotope is mixed evenly with the rest of the liquid in the vial.

Therefore, the fraction of the total liquid in the vial that the isotope makes up is:
0.1667 mL / 9.0 mL = 0.0185

To deliver a dose of 50. mCi, we need that same fraction of the total liquid to be injected into the patient:
0.0185 x volume of liquid injected = volume of isotope injected = 0.1667 mL
Solving for the volume of liquid injected, we get:
volume of liquid injected = 0.1667 mL / 0.0185
volume of liquid injected = 9.0 mL

Therefore, the amount of liquid to be injected into the patient is 9.0 mL - 0.1667 mL = 8.8333 mL, which is closest to 1.5 mL (rounded to the nearest tenth of a milliliter).

Hence, the answer is B) 1.5 mL.

A Radioactive Isotope in a 9