# Nuclear Reactions

So if gravity can't power the sun, how about processes inside an atom? We have two choices here:

1. Chemical reactions (ie reactions dealing with atomic bonds between atoms and electrons)

• Typical energy per atom of around 10 electron volts (the amount of energy stored in the atomic levels of hydrogen and helium).
• Not enough energy to power the Sun for very long (less than gravity!)
2. Nuclear reactions (reactions between atomic nuclei)
• Typical energies are millions of times larger than for chemical reactions.
• Lots of energy available!
So time for a little NUCLEAR PHYSICS (woo-hoo!)

## Inside the Atom

Let's look at Hydrogen and Helium (98% of the Sun) At the center of the Sun, the temperature is high enough that Hydrogen and Helium (and just about everything else) is ionized -- the electrons are no longer bound (attached) to the atoms. We just deal with bare nuclei.

Let's do a few definitions to make life easier.
First define the atomic mass unit as being 1/12 of the mass of the carbon-12 atom:

1 AMU = 1.660540x10-27 kg
Next, bring Einstein into the picture. Einstein realized that E=mc2. Mass and energy are equivalent, related by the speed of light, c.

So we can also talk about mass in terms of energy:

1 AMU =~ 931.5 million electron Volts (MeV)

(where 1 eV = 1.6x10-19 Joules)

Okay, now how does ionization work? If we add energy to the atom, we break apart the electron from the proton. Let's look at this from a mass perspective.

Since a hydrogen atom is simply a proton plus and electron, the mass of the hydrogen atom should simply be equal to the mass if the proton plus the mass of the electron, right?

Wrong!  M(hydrogen) - M(proton) - M(electron) = -13.6 eV

What? What is this energy difference? It is the binding energy of the hydrogen atom.

In other words the correct (schematic) equation is not

hydrogen = proton + electron

But rather

hydrogen + energy = proton + electron

Instead of ionizing atoms, let's look at fusing atoms together.

A hydrogen nucleus is simply a proton.
A helium nucleus is two protons and two neutrons.

We can make helium by fusing together 4 hydrogen atoms. But look:

4 x M(hydrogen) - M(helium) = 26.71 MeV.

Compare this to what happened when we ionized hydrogen:
• The energy difference is MeVs, not eVs. Much bigger.
• The energy left over is positive: energy is produced.
So this time our schematic equation is

hydrogen + hydrogen + hydrogen + hydrogen = helium + energy

So every time you fuse 4 hydrogen atoms together to make helium, 26.7 MeV is released. This is equivalent to about 0.7% of the mass of the 4 original hydrogen atoms.

But is it enough to power the Sun?

Let's estimate how long the Sun could shine by fusing hydrogen into helium.

Assume

• The Sun was originally 100% hydrogen.
• The Sun can only convert the inner 10% into helium.
How much energy is that? Oooh, now we're cooking...

Nothing is free -- what's the problem with fusing hydrogen nuclei?

There are two forces acting inside atoms:

• The electromagnetic force
• Long range
• Coulomb repulsion/attraction
• The strong nuclear force
• Very short range
• Holds the nucleons (protons + neutrons) together
(what are the other two fundamental forces?)

Protons have positive charge. Like charges repel -- the electromagnetic force.
We need to overcome this repulsion to have the nuclei fuse. How do we do this? Energetic nuclei!  How do we make energetic nuclei?