Answer to Question #225861 in Physics for riri

Question

a small amount of radioactive source is injected into a horse. the half-life and the initial activity of the source are 8 days and 3.6x10^5 Bq respectively. after 24 hours, 4 mL of blood is extracted from the horse and the activity recorded is 24Bq. what is the volume of the blood inside the horse? assume the radioactive source distributes uniformly throughout its blood.

Answer 1

The decay constant

$$\lambda=\frac{\ln 2}{t_{1/2}}=\frac{\ln 2}{8*24}=3.61*10^{-3}\:\rm hr^{-1}$$

The activity of the source after 24 hr

$$A=A_0e^{-\lambda t}\\=3.6*10^5*e^{-3.61*10^{-3}*24}=3.3*10^5\:\rm Bq$$

Hence, the volume of the blood inside the horse

$$V=4\rm mL*\frac{3.3*10^5}{24}=5.5*10^4\:\rm mL=55\: L$$