An astrophysical analysis of an ancient lunar basalt sample is conducted to determine its suitability as a historical analog for nuclear fuel. In a commercial thermal reactor, uranium fuel is typically enriched to increase the proportion of the fissile isotope relative to the non-fissile isotope.
Contrast the physical processes that occur when thermal neutrons interact with U-235 nuclei versus U-238 nuclei within a reactor core, describing the distinct outcome for each isotope.
The masses of U-235 and U-238 in the lunar sample decrease over time due to radioactive decay at different rates.
Today, a specific mineral grain within the sample is measured to contain 620 g of U-238.
Show that the mass of U-238 in this sample 3.10×109 years3.10 \times 10^9\text{ years}3.10×109 years ago was approximately 1.00 kg.
decay constant of U-238 =1.54×10−10 year−1= 1.54 \times 10^{-10}\text{ year}^{-1}=1.54×10−10 year−1
A standard thermal nuclear reactor requires a minimum of 3.5% of its total uranium mass to be U-235 to maintain a self-sustaining chain reaction.
3.10×109 years3.10 \times 10^9\text{ years}3.10×109 years ago, the same mineral grain contained 38 g of U-235.
Deduce whether this ancient sample had a high enough U-235 concentration at that time to be used in a thermal nuclear reactor.
