NUCLEAR ENERGY

There are two paths to deriving energy from nuclear reactions - Nuclear Fission and Nuclear Fusion.
First, what is a Nuclear Reaction ?
Remember that the nucleus of every atom is composed of protons ( p⁺ ) and neutrons ( n^o ). If you add or subtract a nucleon to a nucleus, this is a nuclear reaction.
The Forces of Nature
- Gravity is the force that prevents the Sun from expanding despite the fact that it is a hot gas. Gravity also keeps the Earth forever falling towards the Sun in its orbit and keeps all the people in this room in their seats. One way to look at gravity is that it is an attractive force between objects with mass.
- Electric Force is a force felt between charged particles like electrons (e^-) and protons (p⁺). There are both attractive and repulsive electrical forces. Like charges repel, opposite charges attract. The Electrical Force holds atoms and molecules together and is useful for all kinds of nifty gadgets that have been built in the last 150 years.
  Fun note: The electric force is what keeps you from falling through the chair and floor and earth and being cooked in the center of the Earth. You are suspended above your chair by the repulsive force of the protons in your body against the protons in the chair.
- Nuclear Force. If you think about it for a minute, the nuclei of atoms which contain protons (positively charged) and neutrons (no charge) should not be stable. All those "like" charged protons should be repelling one another and fly right out of the nucleus. Since nuclei ARE stable, it can be inferred that there is another force that is stronger than the electrical force which glues those nuclei together. This is the Nuclear Force, or Strong Force. The nuclear force would bind EVERYTHING together except for the fact that it acts only over very tiny distances.

Nuclear Fission

For the "heavy" elements in the Periodic Table, there are some that have nuclei that spontaneously fall apart - these are the radioactive elements. The wild thing about this is that if you weigh the initial nucleus and weigh the bits after the "fission", they don't add to the same total.
The Missing Mass in the fission reaction has been converted into energy via the only equation that 8 out of 10 Americans know:

E = mc²

This equation says that Mass and Energy are interchangable.

Take the mass difference between the Uranium nucleus and the sum of the Thorium and Helium nuclei, multiply by the speed of light squared and you have the amount of energy that was converted from mass in the reaction (released in the form of gamma rays).
The equation above as applied to this reaction (and also to chemical reactions) is:

E = mc²
where m is the mass difference between the Uranium nucleus and the fission product nuclei.
This is a pretty efficient source of energy. Some fission reactions release as much as 10¹⁸ ergs/gram of fissionable material. The problem is that the Sun has only a tiny fraction of its composition in radioactive materials.

THE ANSWER: NUCLEAR FUSION

There is another way to derive energy from nuclei. Think about a gas of protons. At "low" temperatures, the electrical repulsion between them prevents the close approach of any two protons. But as the temperature of the gas increases, the minimum approach distance decreases, and occasionally two protons (10^-15 meters) approach close enough so that the short-range but very strong nuclear attractive force will bind or fuse the protons together.
When two protons fuse, a chargeless, perhaps massless particle called a neutrino is spit out, and one of the protons emits an anti-matter particle called a positron (e⁺) - like a positively charged electron. Having lost its electrical charge, the proton becomes a neutron.

The shorthand for this reaction is:
¹H₁ + ¹H₁²H₁ + e⁺ + ^o

There is a short string of similar reactions that go on in any hot gas of hydrogen atoms. This is called the proton-proton cycle or the P-P cycle.

Step I:	¹H₁ + ¹H₁ ²H₁ + e⁺ + ^o
Step II:	¹H₁ + ¹H₁ ³He₂ +
Step III:	³He₂ + ³He₂ ⁴He₂ + ¹H₁ + ¹H₁ +

The whole thing can be summarized with one net reaction:

4¹H₁ ⁴He₂ + 2 ^o + Energy ( )

Here is the amazing thing:

Mass (4H)	=	6.6943 x 10^-24 grams
Mass (⁴He₂ + 2 ^o)	=	6.6466 x 10^-24 grams

So, 0.048 x 10^-24 grams of matter disappear in the P-P chain.

This mass has been converted into energy (gamma rays). For one reaction, the energy released is:

E	=	0.048 x 10^-24	grams x c²
	=	4.3 x 10^-5	ergs

For every 4 hydrogen atoms (6.7 x 10^-24 grams) we get this much energy out of the reaction, so we can calculate the efficiency of the P-P chain, and compare it to the efficiency of coal power and gravitational potential energy:

6.4 x 10¹⁸	ergs/gram	from P-P Chain
1 x 10¹⁵	ergs/gram	from GPE conversion
4 x 10¹²	ergs/gram	from chemical burning

The Sun and Nuclear Fusion

Now let's suppose the Sun is made of Hydrogen and it is hot enough to run the P-P Chain. How long would its lifetime be at L as a nuclear-fusion powered object?

The available energy from hydrogen fusion is:

(6.4 x 10¹⁸ ergs/grams) x (2 x 10³³ grams) = 12.8 x ⁵¹ ergs
The lifetime of the Sun with fusion power would be:

12.8 x 10⁵¹ ergs x 1 sec
= 3.2 x 10¹⁸ seconds

4 x 10³³ ergs

= 10¹¹ years

Looks pretty promising!
Is Hydrogen Fusion for real or just another theory?

It's for real - don't forget Bikini Atoll which was the nuclear proving ground for the atom bomb.

12.8 x 10⁵¹ ergs x	1 sec	=	3.2 x 10¹⁸ seconds
	4 x 10³³ ergs