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.
