A standard nuclear power plant generates 3.0 GW of thermal...

A standard nuclear power plant generates $3.0 \mathrm{GW}$ of thermal power from the fission of ${ }^{235}$ U. Experiments show that, on average, 0.19 u of mass is lost in each fission of $a^{235}$ U nucleus. How many kilograms of ${ }^{235}$ U undergo fission each year in this power plant?

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Key Concepts

Nuclear Fission

Nuclear fission is the process in which a heavy nucleus splits into two or more smaller nuclei along with the release of a significant amount of energy. In power plants, controlled fission reactions in materials like uranium-235 are used to generate thermal energy, which is then converted to electrical power.

Mass-Energy Equivalence

Mass-energy equivalence, encapsulated in Einstein’s equation E=mc², is the principle that mass and energy are interchangeable. In the context of nuclear fission, the loss of a small amount of mass is converted into a large amount of energy, which is critical for calculating the energy output from the reaction.

Atomic Mass Unit (u)

The atomic mass unit is a standard unit used to express the masses of atoms and subatomic particles. It allows scientists to quantify the small mass differences, or mass defects, that occur during nuclear reactions and to relate these differences to the energy produced via mass-energy equivalence.

Energy Conversion and Units

Energy conversion and the use of proper units are essential for relating the energy produced in nuclear reactions to practical measures, such as thermal power output. This includes converting between units like gigawatts, joules, and years, which is necessary for understanding the energy produced over time in a power plant.

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