Question

The normal concentration of calcium (Ca) in “hard” bone is about 22.5% by mass. You perform the following NAA experiment to verify this number. Ca has several stable isotopes. One of these is 48Ca which has an atomic percent abundance of 0.187% (not mass percent) and a thermal neutron microscopic cross section for the (n,γ) capture reaction of 1.1 barns. Activated 49Ca decays with T1/2 = 8.72min emitting a 3.084 MeV gamma-ray with 92.1% abundance. The absolute peak efficiency of your HPGe detector is 2% at that photon energy. - What saturated activity (Asat) of radioactive 49Ca could you produce if you exposed a 5 gram sample of cortical bone to a thermal neutron flux of 1012 n cm-2 s-1? - How long would it take you to irradiate the sample to 99% of Asat? - If you irradiated the sample to its saturated activity and counted the sample for 20 hours on your HPGe detector, starting the count some 30 minutes after the neutron irradiation, how many full-energy peak counts would you expect to find in your gamma spectrum at 3.084 MeV? Atomic mass of Ca = 40.078 g/mol