A small quantity of solution containing `Na^24` radio nuclide `(half-life=15 h)` of activity `1.0 microcurie` is injected into the blood of a person. A sample of the blood of volume `1cm^3` taken after `5h` shows an activity of `296` disintegrations per minute. Determine the total volume of the blood in the body of the person. Assume that the radioactive solution mixes uniformly in the blood of person.
(1 curie `=3.7 xx 10^10` disintegrations per second)

Explanation

To solve the problem, we will follow these steps:

### Step 1: Convert the initial activity from microcuries to disintegrations per second.
Given:
- Initial activity \( A_0 = 1.0 \, \mu \text{Ci} = 1.0 \times 10^{-6} \, \text{Ci} \)
- Conversion factor: \( 1 \, \text{Ci} = 3.7 \times 10^{10} \, \text{disintegrations/second} \)

Calculating \( A_0 \):
...