Question

A $\mathbf{0}\mathbf{.}\mathbf{10}\mathbf{-}{\mathbf{cm}}^{\mathbf{3}}$sample of a solution containing a radioactive nuclide counts per minute per millilitre) is injected into a rat. Several minutes later,$\mathbf{1}\mathbf{.}\mathbf{0}{\mathbf{cm}}^{\mathbf{3}}$of blood is removed. The blood shows 48 counts of radioactivity per minute. What is the volume of blood in the rat? What assumptions must be made in performing this calculation?

Short answer

• First assumption radioactive nuclide is long-lived.
• Second assumption: radioactivity is evenly distributed throughout the rat's body.

$V=10\mathrm{mL}$

Step-by-step solution

Radioactive decay

The unstable atom’s nucleus loses energy producing radiation, which is known as radioactivity.

A little amount of Uranium compound was wrapped in black paper and put in a drawer containing photographic plates. After further examination of these plates, it was discovered that there had been an exposure.

The term "radioactive decay" was used to describe this occurrence.

The first assumption at half-life.

The amount of radioactive decay injected is:

$\begin{array}{l}=0.10\mathrm{mL}\times \frac{5.0\times {10}^3\mathrm{cpm}}{\mathrm{cpm}}\\ =5.0\times {10}^2\mathrm{cpm}\end{array}$

The second assumption.

The volume of injected blood is evaluated as:

$\begin{array}{c}V\times \frac{48\mathrm{cpm}}{\mathrm{mL}}=5.0\times {10}^2\mathrm{cpm}\\ V=\frac{5.0\times {10}^2\mathrm{cpm}}{48\mathrm{cpm}/\mathrm{mL}}\\ V=10.4\mathrm{mL}\\ V=10\mathrm{mL}\end{array}$

Thus, the first assumption is radioactive nuclide is long-lived. The second assumption is radioactivity is evenly distributed throughout the rat's body.