The natural abundance of deuterium in water is 0.0156 %...

The natural abundance of deuterium in water is $0.0156 \%$ (i.e., $0.0156 \%$ of the hydrogen nuclei in water are ${ }^{2} \mathrm{H}$ ). If the fusion reaction $\left({ }^{2} \mathrm{H}+{ }^{2} \mathrm{H}\right)$ yields $3.65 \mathrm{MeV}$ of energy on average, how much energy could you get from $1.00 \mathrm{L}$ of water? (There are two reactions with approximately equal probabilities; one yields $4.03 \mathrm{MeV}$ and the other 3.27 MeV.) Assume that you are able to extract and fuse $87.0 \%$ of the deuterium in the water. Give your answer in kilowatt hours.

Key Concepts

Efficiency of Fuel Utilization

Efficiency of fuel utilization is the fraction of the available fuel (such as deuterium extracted from water) that is actually used in the energy-producing reaction. This concept is crucial, as practical limits on extraction and reaction rates reduce the potential energy yield from a given quantity of fuel.

Unit Conversion

Unit conversion is the process of translating energy values from one measurement system to another, for example, from mega-electronvolts (MeV) or joules to kilowatt-hours (kWh). This conversion is necessary to express the energy yield in practical and widely used units for real-world applications.

Reaction Energetics

Reaction energetics deals with the energy released or absorbed during nuclear reactions, often measured in mega-electronvolts (MeV). Knowing the energy per reaction is essential for determining the total energy output when a specific number of fusion events take place.

Deuterium Isotope

Deuterium is an isotope of hydrogen that contains one proton and one neutron. As a fuel in nuclear fusion reactions, deuterium’s natural scarcity relative to protium (ordinary hydrogen) means that even small percentages can be critical when calculating the potential energy output from a given material.

Natural Abundance

Natural abundance refers to the percentage of a particular isotope occurring naturally in an element. It is important in scenarios where only a fraction of the atoms present, such as deuterium in hydrogen, participate in a reaction, affecting the overall yield and energy output.

Nuclear Fusion

Nuclear fusion is the process by which two light atomic nuclei combine to form a heavier nucleus, releasing a significant amount of energy. The fusion of deuterium nuclei, for instance, is a reaction of interest due to its high energy yields, though it requires precise conditions to occur.

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