1. Natural hydrogen consists of 0.015% deuterium D, the remainder being protium H. Estimate the mole fractions of H$_2$O, HDO, and D$_2$O in natural water at equilibrium. 2. CANDU reactors use heavy water as a moderator. Reactor-grade heavy water contains a deuterium:protium ratio of 499:1 or higher. Estimate the mole fractions of H$_2$O, HDO, and D$_2$O in reactor-grade heavy water. 3. If all of the deuterium in the world's oceans could be extracted for use as fuel, how much energy could be produced via D-T fusion? (Assume that plenty of tritium could be obtained by the methods described in Chapter 13.)
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Deuterium (Subscript 1 Superscript 2 Baseline H) is an attractive fuel for fusion reactions because it is abundant in the waters of the oceans. In the oceans, about 0.0106% of the hydrogen atoms in the water (H2O) are deuterium atoms. (a) How many deuterium atoms are there in one kilogram of water? (b) If each deuterium nucleus produces about 7.20 MeV in a fusion reaction, how many kilograms of ocean water would be needed to supply the energy needs of a large country for a year, with an estimated need of 7.60 × 1020 J?
Madhur L.
A fusion reactor using only deuterium for fuel would have the following two reactions taking place in it: ${ }^{2}\mathrm{H}+{ }^{2} \mathrm{H} \rightarrow{ }^{3} \mathrm{He}+n+3.27 \mathrm{MeV}$ and ${ }^{2} \mathrm{H}+{ }^{2} \mathrm{H} \rightarrow{ }^{3} \mathrm{H}+{ }^{1} \mathrm{H}+4.03 \mathrm{MeV}$ The ${ }^{3} \mathrm{H}$ produced in the second reaction reacts immediately with another ${ }^{2} \mathrm{H}$ to produce $${ }^{3} \mathrm{H}+{ }^{2} \mathrm{H} \rightarrow{ }^{4} \mathrm{He}+n+17.7 \mathrm{MeV}$$ The ratio of ${ }^{2} \mathrm{H}$ to ${ }^{1} \mathrm{H}$ atoms in naturally occurring hydrogen is $1.5 \times 10^{-4}.$ How much energy would be produced from 4 liters of water if all of the ${ }^{2} \mathrm{H}$ nuclei undergo fusion?
Deuterium makes up 0.0115$\%$ of natural hydrogen on average. Make a rough estimate of the total deuterium in the Earth's oceans and estimate the total energy released if all of it were used in fusion reactors.
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