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Physics: Produce energy commerically by fusion; Dating using carbon-14 decay

1. (A) Efforts are underway to produce energy commerically by fusion. It is too difficult to produce helium by fusion of protons, as is done in the sun, so we have to start with heavier nuclei such as deuterons. One possible reaction is

Calculate the energy, in MeV, released in this reaction. (4.032 MeV) The abundance of deuterium relative to ordinary hydrogen is 0.016%. This means that in one kg of water, there is 0.0089 mol (or 0.0178 gram) of deuterium. Calculate the energy available from using all of the deuterium in one metric ton (1000 kg) of water for a reaction as the one above. (More energy than this would be available, since the tritium produced is unstable and will eventually decay to He-3, with release of energy). (1.73 x 10^(12) J)

Bonneville Dam is capable of generating slightly over 500 MW of power. For what period of time could a fusion-based power plant generate this much power using deuterium from 1 tonne of water? Assume that 65% of the heat generated by the nuclear reaction is turned into electricity. (This is about the best we can do with commercial gas-fired plants.)

2. Dating using carbon-14 decay is said to be useful for organic matter up to 40,000 years old. What would be the activity (disintegrations per second) of a 10-gram piece of carbon, originally from an organism, that is 40,000 years old? Do you think this would be hard to measure accurately? (0.9 distintegrations/minute or .015 per second. This would be difficult since it is below background from cosmic rays, etc.)

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