The volume of blood in the patient is — Nuclear Chemistry and Radioactivity Chemistry Question

💡 Solution & Explanation

The initial activity is $1260 \text{ dps} = 1260 \times 60 = 75600 \text{ dpm}$. After 5 hours (1/3 of a half-life), the remaining total activity is $A = 75600 \times \left(\frac{1}{2}\right)^{5/15} = 75600 \times \left(\frac{1}{2}\right)^{1/3}$. Given $1.26^3 = 2$, we have $\left(\frac{1}{2}\right)^{1/3} = \frac{1}{1.26}$. Thus, $A = 75600 / 1.26 = 60000 \text{ dpm}$. As activity is $15 \text{ dpm/ml}$, Volume $= \frac{60000}{15} = 4000 \text{ ml} = 4.0 \text{ L}$. Therefore, correct answer is C.