6) Age of the Iceman On September 19, 1991, a German couple hiking in the Italian Alps discovered a body trapped in the ice. Subsequent investigation revealed the remarkably well-preserved body to be that of a Stone Age man. When the carbon-14 dating method was applied to the remains of the Iceman and some of the materials he had carried with him, it was found that the carbon-14 activity was about 0.121 Bq per gram of carbon. Using this information, date the remains of the Iceman. (Half-life of carbon-14=5730 yr). Hint: Remember: 14C/12C = 1.20 x 10-12 in all living organisms 53 404

Which of the following is the correct daughter nucleus associated with the beta decay of 72184Hf? (a) 72183Hf (b) 73183Ta (c) 73184Ta

The mass (M) and the radius (r) of a nucleus can be expressed in terms of the mass number, A. (a) Show that the density of a nucleus is independent of A (b) Calculate the density of a gold (Au) nucleus. Compare your answer to that for iron (Fe).

Assume onefourth of the yield of a typical 320kT strategic bomb comes from fission reactions averaging 200 MeV and the remainder from fusion reactions averaging 20 MeV. (a) Calculate the number of fissions and the approximate mass of uranium and plutonium fissioned, taking the average atomic mass to be 238. (b) Find the number of fusions and calculate the approximate mass of fusion fuel, assuming an average total atomic mass of the two nuclei in each reaction to be 5. (c) Considering the masses found, does it seem reasonable that some missiles could carry 10 warheads? Discuss, noting that the nuclear fuel is only a part of the mass of a warhead.

The naturally occurring radioactive isotope 232Th does not make good fission fuel, because it has an even number of neurons; however, it can be bred into a suitable fuel (much as 238U is bred into 239P). (a) What are Z and N for 232Th? (b) Write the reaction equation for neutron captured by 232Th and identify the nuclide AX produced in n+232ThAX+. (c) The product nucleus β decays, as does its daughter. Write me decay equations for each, and identify the final nucleus. (d) Conform that the final nucleus has an odd number of neutrons, making it a better fission fuel. (e) Look up the halflife of the final nucleus to see if it lives long enough to be a useful fuel.

Suppose you have a pure radioactive material with a half-life of T1/2. You begin with N0 undecayed nuclei of the material at t = 0. At t=12T1/2, how many of the nuclei have decayed? (a) 14N0 (b) 12N0(C) 34N0 (d) 0.707N0 (e) 0.293N0