Chapter 5.5, Problem 2E

Radioisotopes and Cancer Detection. A radioisotope commonly used in the detection of breast cancer is technetium- $\text{99m}$. This radionuclide is attached to a chemical that upon injection into a patient accumulates at cancer sites. The isotope’s radiation is then detected and the site located, using gamma cameras or other tomographic devices.

Technetium- $\text{99m}$ decays radioactively in accordance with the equation $dy/dt=-ky$, with $k=0.1155/h$. The short half-life of technetium- $\text{99m}$ has the advantage that its radioactivity does not endanger the patient. A disadvantage is that the isotope must be manufactured in a cyclotron. Since hospitals are not equipped with cyclotrons, doses of technetium- $\text{99m}$ have to be ordered in advance from medical suppliers. Suppose a dosage of $5\text{millicuries}$ ( $\text{mCi}$) of technetium- $\text{99m}$ is to be administered to a patient. Estimate the delivery time from production at the manufacturer to arrival at the hospital treatment room to be $24\text{hours}$ and calculate the amount of the radionuclide that the hospital must order, to be able to administer the proper dosage.