Radioactive isotopes are often used for medical imaging. Technetium-99m (99mTc) is a particularly popular isotope since it has a short half-life and is easy to make. (The “m” in technetium-99m just means that the nucleus is in a metastable, i.e., excited, state.) Also, 99mTc can be chemically bonded to a number of different compounds and cell types for imaging different parts of the body. 99mTc has a half-life of 6.02 hours. It decays into 99Tc by emitting a gamma ray, with energy 140keV for this problem, assume that 99mTc is present in the body for 2 hours after being injected and then is immediately removed. This assumption is reasonable for certain techniques such as renal scans. (For others, a more complex model of technetium removal is needed.)
a. A typical amount of 99mTc injected for medical imaging is 15.0mCi. Convert this to decays per second, also called becquerels (Bq), the SI unit of activity.
b. What is the number N0 of 99mTc atoms that must be present to have an activity of 15mCi?
c. Using the value of N0 that you calculated in Part B, find the number of decays |ΔN| that occur in 2 hours.
d. The gamma-ray released by each decay carries 140keV of energy. Find the total energy E released by decays in the 2 hours.
e. If the amount of 99mTc that you calculated in Part D were administered to an 80-kg man, staying in his body for 2 hours as described, what would his absorbed dose be in rads?
