Deuterium ( 1 H 2 ) is an attractive fuelfor fusion reactions because it is abun

Question

Deuterium (1H2) is an attractive fuelfor fusion reactions because it is abundant in the waters of theoceans. In the oceans, about 0.197% of the hydrogen atoms in thewater (H2O) are deuterium atoms. (a) How many deuteriumatoms are there in one kilogram of water? (b) If each deuteriumnucleus produces about 7.2 MeV in a fusion reaction, how manykilograms of ocean water would be needed to supply the energy needsof a large country for a year, with an estimated need of 9.1 x 1019 J?
please help me, i really need it. Deuterium (1H2) is an attractive fuelfor fusion reactions because it is abundant in the waters of theoceans. In the oceans, about 0.197% of the hydrogen atoms in thewater (H2O) are deuterium atoms. (a) How many deuteriumatoms are there in one kilogram of water? (b) If each deuteriumnucleus produces about 7.2 MeV in a fusion reaction, how manykilograms of ocean water would be needed to supply the energy needsof a large country for a year, with an estimated need of 9.1 x 1019 J?
please help me, i really need it.

Explanation / Answer

(a)    the number n of atoms of hydrogen and itsisotopes in 1 kg of water is    n = 2 (6.02 x 1023 / mol) (1.00 x103 g) / (18.015 g / mol)       = ..........    if dueterium makes up 0.197 % of hydrogen inthis number of atoms, the number N of dueterium atom is    N = (1.97 x 10-4) (n)        = ........ (b)    each dueterium nucleus provides 7.2 MeV ofenergy so the energy from 1 kg of water will be    E = (N) (7.2 x 106 eV) (1.602 x10-19 C) / (1 eV)        = ....... J    the mass will be    m = (9.1 x 10 19 J) (E)        = .......... kg

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