Deuterium (Subscript 1 Superscript 2 Baseline H) is an attractive fuel for fusio

Question

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 0.0135% 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 8.10 Ý 1020 J?

Explanation / Answer

a)

1000 grams water * 1 mole / 18 grams * 6.022x10^23 molecules / 1 mole =

= 334.56 x 10^23 molecules of water

there are two hydrogen atoms per molecule of water, so in 1 kg of water there are

2 * 334.56 = 669.11x10^23 hydrogen atoms

but only 0.0135% of these are deuterium so there are

0.000135 * 669.11 = 0.0903x10^23 =9.03 x 10^21 deuterium atoms in one kg of water

b)

9.03 x 10^21 atoms * 7.20 MeV / 1 atom * 1.60x10^-13 Joules / 1 MeV =

= 104.03 x 10^8 Joules of energy

so a country would need

8.10 x 10^20 Joules * 1 kg / 104.03 x 10^8 Joules =

= 7.786x 10^10 kg of water

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