# Of all the hydrogen in the oceans, 0.030 0% of the mass is deuterium. The oceans have a volume of 318 million mi3. (a) If nuclear fusion were controlled and all the deuterium in the oceans were...

Of all the hydrogen in the oceans, 0.030 0% of the mass is deuterium. The oceans have a volume of 318 million mi3.

(a) If nuclear fusion were controlled and all the deuterium in the oceans were fused to , how many joules of energy would be released?

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Deuterium undergoes fusion reaction as:

`^2H_1 +^2H_1 --> ^4He_2 + 23.85 MeV`

Amount of energy released per partiicle in the fusion reaction is thus,

23.85 MeV

= 23.85*10˄6*1.60217*10˄-19*6.0222*10˄23 J/mol

= 2301.3 GJ/mol.

Thus, 4 gram deuterium produces 2301.3 GJ energy.

1 gram should produce 2301.3/4 = 575.325 GJ

Assuming the density of sea water to be 1g/cm˄3, total amount of deuterium in sea water is

= 318*10˄6*10˄6*0.030/100 [since 1m˄3 =(100)˄3=10˄6 cm˄3]

= 9.54*10˄10 g

In terms of energy, this is equivalent to

9.54*10˄10*575.325 GJ

= 5.489*10˄13 GJ.

= 5.489*10˄22 Joules.

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