Nuclear Energy

I have used the notion of energy conservation several times already. However, I now need to expand the notion of energy a little.

As shown by Einstein in the early 1900's:
mass and energy are equivalent, they are simply different forms of one physical quantity. Einstein related these two quantities in the famous relation, E = mc**2.
Note -- For a particle of mass m, we call the quantity mc**2, its rest mass energy.
As a result, we must expand our notion of energy conservation to include the possibility that matter can be turned into radiation and vice versa.

The inverse of the above can also occur. High energy photons can "annihilate" and produce pairs of anti-amtter/matter particles. In the early Universe, such transformations of mass into energy and back into mass were very common.

Now, for convenience, let me define an efficiency for energy production. I will use the annihilation process as my benchmark.

The efficiency is
- e = energy produced / (mass involved x c**2)
For annihilation radiation, the efficiency is e = 1
For chemical burning
- e ~ 2 x 10**(-11) ergs/(30 x m(proton) x c**2) ~ 0.000000005
  where m(proton) = 1.7 x 10**(-24) grams
For the nuclear reactions which power the Sun (4 hydrogens into 1 helium)
- e = 0.007, that is, 0.7 % of the mass is converted into energy

So, we see that the annihilation process is the most efficient and that chemical burning is the least efficient. Although, nuclear fusion is less than 1 % efficient, it is still efficient enough to account for the Sun's luminosity as we now argue.

Hydrogen Burning

We refer to nuclear fusion as a burning process, although strictly speaking, it is not burning. In the Sun, we have,