Question

The volume of water in the Great Lakes is 5000 cubic mile. Calculate the amount of energy released if all the deuterium atoms in water are used up in fusion. Given that the abundance of deuterium is 0.0156% and the fusion of 6 deuterium atoms gives an energy of 43 MeV. Given 1 mile = 1.6 Km

Answer 1

The volume of water in the Great Lakes = 5000 cubic mile

The mass of water = 5000 × (1.6×103)3 ×103 Kg = 2.13 × 1016 kg

Since molecular weight of water is 18, the total number of molecules in water having a mass of 2.13×1016 kg

Since the abundance of deuterium is 0.0156%, we have total number of deuterium atoms is

= 7.13 × 1041× 2 × 0.0156 × 1016 = 2.22×1028

Now the fusion of 6 deuterium atoms gives an energy of 43 MeV, therefore the energy release per atom is

43/6 = 7.17 MeV

Hence the total release of energy of 2.22 × 1028 × 7.17 MeV = 1.6 × 1029 MeV