Each of the following isotopes has been used medically for the purpose indicated. Suggest reasons why the particular element might have been chosen for this purpose. a. cobalt-57, for study of the body's use of vitamin \(\mathrm{B}_{12}\) b. calcium- 47 , for study of bone metabolism c. iron- 59 , for study of red blood cell function

Cobalt-57 is a radioactive isotope with a half-life of about 271.79 days, which decays by gamma (γ) emission. Vitamin B12 (cobalamin) is an essential nutrient for the body and has a cobalt atom at its center. The reason Cobalt-57 is used for studying the body's use of vitamin B12 is because it can replace the natural cobalt in vitamin B12 and its radioactive properties allow it to be traced in the human body. By introducing the radioactive isotope of cobalt (Cobalt-57) into vitamin B12, researchers can trace its movement, absorption, and distribution in the body through imaging techniques, providing valuable information on how the body utilizes vitamin B12.

Calcium-47 is a radioactive isotope with a half-life of about 4.536 days that decays by beta (β) emission. Calcium is an essential nutrient in the human body and is the primary component of bones and teeth. The reason Calcium-47 is used for studying bone metabolism is because it can replace the stable calcium isotope (Calcium-40) in the bones due to its similar chemical properties. When the radioactive isotope of calcium (Calcium-47) is introduced into the body, the natural calcium balance processes will lead to the incorporation of the isotope into bone tissue. By detecting the radioactive emissions, researchers can measure the rates of bone formation and resorption, providing insights into bone growth and remodeling as well as diagnosing and monitoring bone-related diseases.

Iron-59 is a radioactive isotope with a half-life of about 44.5 days, which decays by beta (β) emission and gamma (γ) emission. Iron is a vital element in the human body, playing a critical role in the function of red blood cells by binding to hemoglobin protein and assisting in oxygen transport. The reason Iron-59 is used for studying red blood cell function is because it can replace the stable isotope of iron (Iron-56) present in hemoglobin, without affecting the normal function of red blood cells. By introducing the radioactive isotope of iron (Iron-59) into the body, researchers can trace where it is incorporated into red blood cells and track the movement, distribution, and lifespan of red blood cells. This information can help diagnose and monitor various blood disorders such as anemia and other hematological conditions.