A \(0.2 \mathrm{~mL}\) sample of a solution containing \(1.0 \times 10^{-7}\) curie of \(_{1} \mathrm{H}^{3}\) is injected to the blood stream of an animal. After sufficient time for circulatory equilibrium to be established, \(0.10 \mathrm{~mL}\) of blood is found to have an activity of \(20 \mathrm{dpm}\). Calculate the volume of blood in animal, assuming no change in activity of sample during criculatory equilibrium.

Radioactive materials decay over time, releasing particles in a process we measure using units of radioactivity. One such unit is the curie (Ci), which historically represented the radioactivity of one gram of radium-226. In modern terms, a curie is a huge amount of radioactivity, equivalent to 3.7 x 10¹⁰ disintegrations per minute (dpm).

To convert from curies to dpm, you use the following formula: \
\( \text{Activity in dpm} = \text{Activity in curies} \times 3.7 \times 10^{10} \text{ dpm/curie} \).

This conversion is crucial in biomedical applications like radioactive tracer techniques, where precise measurements determine the administered dosage for imaging or treatment. Understanding the conversion ensures safety and accuracy in these medical procedures.

Disintegrations per minute (dpm) is a unit used to describe the rate at which radioactive atoms decay. In a given sample of a radioactive substance, not all of the atoms will decay at once, but rather at a predictable and steady rate. This rate is measured by counting how many atoms disintegrate each minute.

For example, if a sample has an activity of 20 dpm, it means that 20 atoms are decaying and releasing particles every minute. This metric is important not only for scientific research but also for medical applications, such as determining the proper radioactive dose in treatments or diagnostics.

Circulatory equilibrium refers to a stage in tracer studies when the distribution of the radioactive tracer throughout the circulatory system of the organism becomes uniform. After the tracer is injected, it mixes with the blood and circulates through the body.

Once circulatory equilibrium is achieved, the concentration of the radioactive tracer should be consistent throughout the entire volume of blood. This state allows scientists or healthcare providers to calculate the total volume of blood by using the measures of radioactivity per unit volume of blood sample collected. It's also assumed that the activity of the tracer does not change during this time, which simplifies calculations and helps ensure the accuracy of the results.