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 0.0141% 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 8.60 × 1020 J?

Explanation / Answer

number of hydrogen atoms in 1 mole = 18 g of water = 2 x 6.023 x 1023 atoms

18 g of water = 2 x 6.023 x 1023 atoms

number of hydrogen atoms in 1000 g of water = 2 x 6.023 x 1023 (1000/18) = 6.7 x 1025 atoms

Number of deuterium atoms = n = (0.0141/100) (6.7 x 1025 ) = 9.45 x 1021 atoms

b)

total energy needed = Etotal = 8.60 × 1020 J

Energy provided by each nucleus = 7.20 x 106 x 1.6 x 10-19 = 1.152 x 10-12 J

Number of nulceus needed = N = (8.60 × 1020 ) / (1.152 x 10-12 ) = 7.5 x 1032

1 kg of water provides = 9.45 x 1021 atoms

9.45 x 1021 atoms = 1 kg water

7.5 x 1032 atoms = (1/(9.45 x 1021 ) ) (7.5 x 1032 ) = 7.94 x 1010 kg of water

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