The Physics of Energy
 Missing Mass and Einstein's Theory of Relativity Einstein's Theory of Relativity explains how fusion could yield an enormous amount of energy for human use - a whopping 5.00 × 108 Kilojoules from 1 gram of deuterium, enough to last us for hundreds of thousands of years. In order to understand Einstein's theory, we need to do some simple arithmetic. In any chemistry textbook (or a good encyclopedia) we can discover that a proton has a mass of 1.6726 × 10-24 grams, a neutron 1.6755 × 10-24 grams, an electron 9.109 x 10-28 grams, a deuterium atom 3.345 × 10-24 grams and a tritium atom 5.01 × 10-24 grams. Okay, so now we have the masses of all the reactants in a fusion reaction. Next, we need to find the masses of the products. We know that a helium atom and a neutron are produced in the reaction. A helium atom has 2 protons, 2 neutrons, and 2 electrons: 2(1.6726 × 10-24 grams) + 2(1.6755 × 10-24 grams) + 2(9.109 x 10-28 grams) = 6.698 x 10-24 grams And of course, the mass of the freed neutron is just 1.6755 × 10-24 grams All that's left is to add the masses of the reactants and see if the sum matches the sum of the masses of the products. So 1 tritium + 1 deuterium should equal 1 helium + 1 neutron 3.345 × 10-24 g + 5.01 × 10-24 g should equal 6.698 x 10-24 g + 1.6755 × 10-24 g so... 8.3549 × 10-24 g should equal 8.3735 × 10-24 g But instead there is a difference of about 1.86 × 10-26 g Why aren't the two values equivalent? Even though the difference is extremely small, we must remember that the disparity in mass is for only 1 atom each of deuterium and tritium. If, for instance, there had been one gram of deuterium and a proportionate amount of tritium, the mass difference produced would have been about 0.00556 grams, quite a significant amount! Now that we know that there is in fact a difference in the masses, we can put Einstein's equation to good use. E=mc2. What does that famous equation actually mean? Well, to put it simply, Einstein's theory relates mass and energy. We've all heard the statement that mass and energy can neither be created nor destroyed. But what about the missing mass in the fusion equation? According to Einstein, that mass has actually been directly converted to energy. Since E=mc2, where "m" is mass and "c" is the speed of light (3.00 × 108 m/s), E = (1.86 × 10-26 g)(3.00 × 108 m/s)2 so E = 1.674 × 10-9 g m/s = 1.674 × 10-12 kg m/s E = 1.674 × 10-12 Joules/atom Using the 1 gram of deuterium example again, the energy produced by fusion would be a whopping 5.00 × 108 Kilojoules, approximately equivalent to the energy produced by the combustion of 2400 gallons of oil.