3. Since the half life of U-235 (7.13E8 yrs.) is less than the half life of...

 

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3. Since the half life of U-235 (7.13E8 yrs.) is less than the half life of U-238 (4.51E9 yrs.) the isotopic abundance of U-235 has been decreasing relative to U-238 since the earth was formed about 4.5 billion years ago. Fission products have been found which indicate that natural reactors have existed in Africa (read Sec 4.9). This would likely have required the enrichment to be about 3.0 a/o. Currently U-235 is only 0.72 a/o or 0.711 w/o of natural U. Estimate how many years ago the natural enrichment of Uranium was 3.0 a/o. Note that a rigorous calculation would require accounting for the mass difference between U-235 and U238, and for the decay of U-238 For this estimate ignore the weight difference and decay of U-238 and assume they are equal. I will provide a rigorous calculation in review of this problem. 4. For reactor calculations it is very important to know the atom densities of all the isotopes in the reactor since each isotope reacts differently with neutrons. A typical power reactor fuel is uranium enriched to about 4.95 w/o U-235. Fuel in a reactor is typically U02 with a density of 10.5 g/cm cubed. What is the atom density of U-235 in the fuel? See example 2.16 in Section 2.14 and remember to account for the oxygen in UO2 3. Since the half life of U-235 (7.13E8 yrs.) is less than the half life of U-238 (4.51E9 yrs.) the isotopic abundance of U-235 has been decreasing relative to U-238 since the earth was formed about 4.5 billion years ago. Fission products have been found which indicate that natural reactors have existed in Africa (read Sec 4.9). This would likely have required the enrichment to be about 3.0 a/o. Currently U-235 is only 0.72 a/o or 0.711 w/o of natural U. Estimate how many years ago the natural enrichment of Uranium was 3.0 a/o. Note that a rigorous calculation would require accounting for the mass difference between U-235 and U238, and for the decay of U-238 For this estimate ignore the weight difference and decay of U-238 and assume they are equal. I will provide a rigorous calculation in review of this problem. 4. For reactor calculations it is very important to know the atom densities of all the isotopes in the reactor since each isotope reacts differently with neutrons. A typical power reactor fuel is uranium enriched to about 4.95 w/o U-235. Fuel in a reactor is typically U02 with a density of 10.5 g/cm cubed. What is the atom density of U-235 in the fuel? See example 2.16 in Section 2.14 and remember to account for the oxygen in UO2