Fusion and stars - Physics - IB Diploma Programme

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E.5 Fusion and stars •

Hello future astrophysicists! In this final section of Nuclear Physics, we explore the most powerful energy source in the universe: Nuclear Fusion. This is the process that lights up the sky—it is how the Sun and all other stars generate their incredible, sustained energy. Understanding fusion helps us grasp the sheer scale of the universe and provides crucial context for why certain elements exist.

1. The Physics of Nuclear Fusion

Fusion is the opposite of Fission (E.4). While fission involves splitting heavy nuclei, fusion is the process of combining light nuclei to form a heavier, more stable nucleus.

Definition and Process

Nuclear Fusion: A reaction where two or more atomic nuclei collide at very high speeds and temperatures to form a single, heavier nucleus.
This process releases massive amounts of energy because the resulting nucleus is more stable than the initial nuclei combined.

Analogy: Think of fusion as merging two small, unstable boats (light nuclei) into one large, perfectly balanced super-tanker (the heavier, stable nucleus). This merger requires energy initially, but the resulting structure is much more locked-in and stable.

The Role of Binding Energy

To understand why fusion releases energy, we must look at the Binding Energy per Nucleon (BEN) curve (which you studied in previous sections of Nuclear Physics).

The BEN curve shows that stability increases as the BEN value increases, peaking around the element Iron (\(^{56}Fe\)).
For elements lighter than Iron, combining them (fusion) causes the new nucleus to have a higher BEN.
When the BEN increases, energy is released. Fusion takes light elements (like hydrogen) and moves them up the stability curve towards iron.

Quick Takeaway: Fusion happens when the product nucleus is more tightly bound (has a higher BEN) than the reactants, resulting in a net release of energy.

2. Energy Release: Mass Defect and \(E=mc^2\)

The energy released during fusion is a direct consequence of the Mass Defect, explained by Einstein’s famous mass-energy equivalence equation.

The Calculation Principle

When light nuclei fuse, the mass of the resulting nucleus is measurably less than the sum of the masses of the original nuclei. This lost mass is the Mass Defect (\(\Delta m\)).

The mass defect is converted into pure energy according to the formula: \[ E = \Delta m c^2 \] Where:
- \(E\) is the energy released (in Joules).
- \(\Delta m\) is the mass defect (in kilograms).
- \(c\) is the speed of light in vacuum (\(3.00 \times 10^8 \text{ m/s}\)).
Because \(c^2\) is a huge number (\(9 \times 10^{16}\)), even a tiny mass defect results in an enormous energy release.

Common Mistake to Avoid: Students sometimes assume fusion means mass is *gained*. Remember, the final nucleus is heavier than the individual *reactants*, but the *total mass* of the system decreases, giving us the mass defect and the released energy!

3. The Essential Conditions for Fusion

If fusion releases so much energy, why is it so hard to achieve here on Earth? The answer lies in overcoming the natural repulsive forces between nuclei.

The Coulomb Barrier

All atomic nuclei contain positively charged protons. Because like charges repel, when you try to push two nuclei together, they experience a very strong electrostatic repulsion force. This repulsive force is called the Coulomb Barrier.

Requirement 1: Extremely High Temperature

To overcome the Coulomb Barrier, the nuclei must approach each other extremely closely (within the range of the short-range strong nuclear force).

This requires the nuclei to have immense kinetic energy.
High kinetic energy means extremely high speed, which translates directly to extremely high temperature.
The core of the Sun operates at about 15 million Kelvin, providing the energy needed for fusion.

Analogy: Imagine trying to stick the North poles of two powerful magnets together. You have to slam them together incredibly hard and fast to get them close enough for the glue (the strong nuclear force) to kick in and hold them. The speed you use is analogous to the high temperature required.

Requirement 2: High Density/Pressure

Even at high temperatures, the probability of two nuclei colliding exactly right is low. To sustain a reaction, you need a high collision rate.

High density ensures there are enough nuclei packed close together so that collisions occur frequently enough to sustain the reaction.
In stars, this density is provided by the massive gravitational pressure exerted by the overlying layers of stellar material.

Did you know? On Earth, scientists working on controlled fusion (like in tokamaks) must contain the super-hot material using massive magnetic fields, as no physical container could withstand the heat.

Key Takeaway: Fusion requires overcoming the Coulomb Barrier, necessitating millions of degrees Kelvin and immense pressure/density.

4. Fusion in Stars: The Sun’s Engine

The Sun, being primarily made of hydrogen, uses hydrogen nuclei (protons) as its primary fuel source.

Stellar Fuel and Plasma

In the extreme conditions of a stellar core, matter does not exist as a neutral gas. The high temperatures strip the electrons from the atoms, creating a soup of free nuclei and electrons called Plasma.

Plasma is often referred to as the "fourth state of matter."
All fusion reactions in stars occur within this plasma core.

The Proton-Proton Chain (pp chain)

The most common fusion process occurring in stars like our Sun is the Proton-Proton (pp) chain. This is a sequence of reactions that slowly builds up helium from hydrogen.

Don't worry if the exact intermediate steps seem complex—for IB Physics, focus on the net result and the overall physics principles involved.

The Net Reaction Summary:

Four hydrogen nuclei (protons) are converted into one helium nucleus.
Input: 4 H-1 nuclei (\(4 \times {}_{1}^{1}H\))
Output: 1 He-4 nucleus (\({}_{2}^{4}He\)) + 2 positrons (\(2 \times e^{+}\)) + 2 neutrinos (\(2 \times \nu\)) + Energy (gamma rays and kinetic energy).

Sustaining the Star

The immense energy released by this fusion process provides the outward radiation pressure that perfectly balances the inward force of gravitational contraction. This balance keeps the star stable and determines its size and lifespan. Our Sun has been stable for about 4.5 billion years and will continue fusing hydrogen for roughly another 5 billion years.

Quick Review Box: Fusion and Stars (E.5)

Key Concepts in E.5:

Fusion: Combining light nuclei to increase Binding Energy per Nucleon (BEN).
Energy Source: Release of energy due to Mass Defect (\(\Delta m\)) via \(E = \Delta m c^2\).
Challenge: Overcoming the Coulomb Barrier (electrostatic repulsion).
Conditions: Requires extremely high Temperature (Kinetic Energy) and Density/Pressure.
Stellar Process: The Sun uses the Proton-Proton Chain to convert Hydrogen into Helium in a Plasma state.