A certain shale deposit containing 0.006 % U by mass is...

A certain shale deposit containing $0.006 \%$ U by mass is being considered for use as a potential fuel in a breeder reactor. Assuming a density of $2.5 \mathrm{g} / \mathrm{cm}^{3},$ how much energy could be released from $1.00 \times 10^{3} \mathrm{cm}^{3}$ of this material? Assume a fission energy of $3.20 \times 10^{-11} \mathrm{J}$ per fission event (that is, per U atom).

Key Concepts

Nuclear Fission

Nuclear fission is the process in which a heavy atomic nucleus splits into lighter nuclei, releasing a significant amount of energy. In the context of reactor fuel, each fission event contributes a fixed amount of energy, making it crucial to determine the number of available fissile atoms in order to estimate the total energy output.

Energy per Fission Event

This concept refers to the specific, known amount of energy released when a single uranium atom undergoes fission. It acts as a conversion factor between the number of fission events (or fissile atoms) and the total energy produced, allowing one to calculate the aggregate energy yield from a given mass of uranium.

Mass Density and Volume Conversion

Density is used to relate the volume of a material to its mass. By knowing the density and the volume of the shale deposit, one can compute the total mass of the material, which is a necessary step in determining the amount of uranium present in the deposit.

Percent Composition by Mass

This concept involves calculating the fraction of the total mass that is comprised of a specific component – in this case, uranium. Converting a percentage into a mass fraction allows you to determine the absolute mass of uranium in a given sample of the shale deposit.

Mole Concept and Avogadro's Number

The mole concept links the macroscopic mass of a substance to the number of constituent particles, such as atoms. Avogadro's number provides the conversion factor between moles and individual atoms. This is essential for converting the mass of uranium into the number of uranium atoms, which then can be multiplied by the energy per fission event to estimate the total energy released.

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