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 0.0119% 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 7.90 × 1020 J?

Answer 1

1 kg of water contains 1000 gr/ 18 (MW) = 55.55 moles of water.

every mole of water contains 2 x avagadro number of hydrogen atoms.

avagadro number = N_A = 6.02x10²³

so 55.55 moles of water contains = 111.1xN_A hydrogen atoms.

so 0.0119% of 111.1xN_A = 0.0132209xN_A deuterium atoms available per Kg of water.

NOTE 1J = 6.241509x10¹⁸ ev

7.90 × 10²⁰ J = 6.241509x10¹⁸ x 7.90 × 10²⁰ = 49 x 10 ³⁸   ev

one dueterium nucleus = one deuterium atom, gives 7200000 ev energy

number of deuterium atoms required = 49 x 10 ³⁸ / 7200000 = 0.68 x 10 ³³

water required = 0.68 x 10 ³³ / (0.0132209xN_A) = 51.475x 10 ³³ /N_A kg of water.=8.551x 10 ¹⁰ kg of water