#2709 Nuclear Fission

#2709 Where does the energy from fission come from?

The energy from fission comes from the binding energy of an atomic nucleus, which is the energy required to hold the nucleus together. Here's a breakdown:

Binding Energy and Mass Defect:
- Atomic nuclei are composed of protons and neutrons (nucleons), held together by the strong nuclear force.
- When a nucleus splits during fission, the total mass of the resulting fragments and free neutrons is slightly less than the original mass of the parent nucleus. This difference in mass is called the mass defect.
- According to Einstein's famous equation, $E = mc^2$ , this mass defect is converted into energy.
Mechanism of Fission:
- Fission occurs when a heavy nucleus (like uranium-235 or plutonium-239) absorbs a neutron and becomes unstable.
- The unstable nucleus deforms and splits into two smaller nuclei (fission fragments), releasing free neutrons and energy.
- The energy released includes:
  - Kinetic energy of the fission fragments (the largest component).
  - Energy of emitted neutrons.
  - Energy carried away by gamma rays (electromagnetic radiation).
  - Energy from the decay of radioactive fission products.
Scale of Energy Release:
- The energy released per fission event is approximately 200 million electron volts (MeV).
- This is millions of times more energy per atom than chemical reactions like combustion, making fission a powerful energy source.

In essence, the energy from fission comes from the conversion of a small fraction of nuclear mass into energy, governed by the principles of nuclear physics.

What elements are fissionable?

Fissionable elements are those whose nuclei can undergo nuclear fission. They are generally heavy elements with large atomic masses and numbers. These elements are divided into two main categories based on how they interact with neutrons:

1. Fissionable Elements

These elements can undergo fission when struck by a high-energy (fast) neutron but are not necessarily capable of sustaining a chain reaction with thermal (slow) neutrons.

Examples:
- Uranium-238 ( $^{238}U$ )
- Thorium-232 ( $^{232}Th$ )

2. Fissile Elements

Fissile elements are a subset of fissionable elements that can sustain a chain reaction because they undergo fission when struck by thermal (slow) neutrons.

Examples:
- Uranium-235 ( $^{235}U$ )
  - Naturally occurring in small amounts.
- Plutonium-239 ( $^{239}Pu$ )
  - Produced from uranium-238 in reactors.
- Uranium-233 ( $^{233}U$ )
  - Produced from thorium-232 in reactors.

3. Fertile Elements

These elements are not directly fissionable with thermal neutrons but can be converted into fissile isotopes through neutron absorption followed by radioactive decay.

Examples:
- Uranium-238 ( $^{238}U$ ) → Plutonium-239 ( $^{239}Pu$ )
- Thorium-232 ( $^{232}Th$ ) → Uranium-233 ( $^{233}U$ )

Synthetic Fissionable Materials

Some isotopes of heavier transuranic elements (produced in reactors or accelerators) are also fissionable, such as:

Neptunium-237 ( $^{237}Np$ )
Curium-245 ( $^{245}Cm$ )

Summary

In practical nuclear power and weapons:

Fissile elements ( $^{235}U, ^{239}Pu, ^{233}U$ ) are most important because they enable chain reactions with thermal neutrons.
Fertile elements ( $^{238}U, ^{232}Th$ ) are important in breeder reactor technology, where they are converted into fissile isotopes.

Why so limited a group?

The group of fissionable and fissile elements is limited because of the specific nuclear properties required for fission to occur effectively. These properties arise from the interplay of nuclear forces, stability, and the behavior of neutrons. Here's why the group is so restricted:

1. Nuclear Size and Binding Energy**

Heavy nuclei (large atomic numbers like uranium and plutonium) have a large number of protons, leading to significant repulsive forces between them due to their positive charges.
The strong nuclear force, which holds the nucleus together, becomes less effective over longer ranges in very large nuclei.
As a result, heavy nuclei are closer to instability and can split (fission) when disturbed, especially by neutron absorption.

Smaller nuclei, on the other hand, are far more stable because the strong nuclear force dominates over electrostatic repulsion. They don’t undergo fission easily or at all.

2. Neutron Absorption Cross-Section**

For fission to occur, a nucleus must effectively capture a neutron. This is quantified by the neutron absorption cross-section:
- Fissile isotopes like $^{235}U$ and $^{239}Pu$ have high absorption cross-sections for slow (thermal) neutrons, making them useful for chain reactions.
- Non-fissile isotopes (e.g., $^{238}U$ ) require fast, high-energy neutrons to fission and cannot sustain a chain reaction under normal reactor conditions.

This property narrows the field of useful elements to a few specific isotopes.

3. Stability of Nuclei**

The elements eligible for fission are inherently unstable because of their large proton-to-neutron ratios. However, the vast majority of heavy elements are too stable to fission easily and instead decay slowly via alpha decay or other radioactive processes.
Fissile isotopes are rare exceptions where nuclei are just unstable enough to undergo fission with thermal neutrons.

4. Rarity of Naturally Occurring Isotopes**

Only a few isotopes occur naturally in significant quantities:
- Uranium-235 is the only naturally occurring fissile isotope in appreciable quantities (~0.7% of natural uranium).
- Uranium-238 and Thorium-232 are abundant but need to be converted into fissile isotopes like $^{239}Pu$ or $^{233} U in reactors (breeder technology).$
Most other fissionable isotopes are synthetic (e.g., $^{239}Pu$ , $^{233}U$ ) and require nuclear reactors for production.

5. Chain Reaction Requirements**

To sustain a nuclear chain reaction, the material must produce more neutrons than are absorbed or escape during fission. This neutron economy is a delicate balance:
- Fissile isotopes like $^{235}U$ and $^{239}Pu$ release sufficient neutrons to maintain the reaction.
- Non-fissile isotopes generally do not meet this criterion.

6. Practical Engineering and Safety Constraints**

Even among fissionable materials, only those that can be handled safely, enriched, and used in controlled reactors are viable for energy production or weapons.
Some heavy elements (like curium or californium) are fissionable but are not practical due to their extreme rarity, high radioactivity, or complex production requirements.

Summary

The limited group of fissionable elements is determined by a combination of:

Nuclear instability in heavy nuclei.
Effective neutron absorption and fission probabilities.
The need to sustain a chain reaction.
Natural abundance or ability to produce the element synthetically.

These specific requirements create a small, unique set of isotopes suited for practical use in nuclear power and weapons.

Why is carbon not fissionable?

Carbon is not fissionable because its nuclei do not meet the physical and nuclear conditions required for fission. Here's a detailed explanation:

1. Carbon's Atomic Mass and Stability**

Carbon ( $^{12}C$ ) is a light element with a small atomic number (6 protons) and a low atomic mass (12 atomic mass units for $^{12}C$ , the most abundant isotope).
Fission occurs primarily in heavy nuclei with high atomic numbers (like uranium or plutonium) because these nuclei are inherently less stable due to the repulsive forces between their many protons.
Light elements like carbon are highly stable because:
- The strong nuclear force effectively binds the relatively small number of nucleons together.
- They do not have the large proton-proton repulsive forces seen in heavy nuclei.

2. Binding Energy per Nucleon**

The energy required to hold a nucleus together is known as the binding energy per nucleon.
For light elements like carbon, the binding energy per nucleon is near its maximum (around 8 MeV), making these nuclei extremely stable.
Fission occurs when a nucleus splits into smaller nuclei with higher total binding energy per nucleon, releasing energy. Carbon's binding energy per nucleon is already very high, so splitting it would not result in a net energy release.

3. Neutron Interaction**

Fissionable nuclei must readily absorb neutrons to initiate fission.
Carbon nuclei have a low neutron absorption cross-section, meaning they do not easily capture neutrons.
Even if a carbon nucleus were to absorb a neutron, it would not become unstable enough to undergo fission. Instead, it might emit a gamma ray or undergo another non-fission process.

4. Insufficient Mass for Energy Release**

Fission is only energetically favorable in heavy nuclei because they release significant energy when split into smaller fragments.
For light nuclei like carbon, the energy required to split the nucleus exceeds the energy that would be released. This makes fission energetically unfavorable.

5. Carbon's Role in Nuclear Physics**

While carbon is not fissionable, it does have important roles in nuclear physics:

Carbon-12 and Carbon-13 are stable isotopes and do not undergo fission.
Carbon-14 is radioactive but decays via beta decay, not fission.
Carbon is often used as a moderator material in nuclear reactors to slow down neutrons (thermalize them), making them more likely to cause fission in fissile materials like uranium-235.

Summary

Carbon is not fissionable because it is a small, highly stable nucleus with:

A low atomic number and small size.
High binding energy per nucleon, making fission energetically unfavorable.
Low neutron absorption cross-section.
Insufficient energy gain from splitting.

Fission is a process reserved for heavy, unstable nuclei like uranium or plutonium, which carbon does not qualify as.

So, it is impossible to fission carbon?

No, it is not impossible to fission carbon, but it is extremely unlikely and impractical under normal conditions. Here's why:

1. Fission of Carbon Is Theoretically Possible

In principle, any nucleus, including carbon, can undergo fission if it absorbs enough energy to overcome the binding forces holding it together. However:
- For carbon ( $^{12}C$ , the most common isotope), this requires a massive input of energy, far beyond what is typically available in a nuclear reaction.
- Carbon nuclei are very stable, and the conditions needed to force fission are extreme.

2. Carbon Under High-Energy Conditions

Carbon nuclei can break apart in extremely high-energy environments, such as:
- Cosmic rays or particle accelerators: When bombarded with very high-energy particles, carbon nuclei can be shattered into smaller fragments.
- Nuclear reactions involving very high neutron or proton fluxes: In rare cases, high-energy neutron bombardment can break a carbon nucleus, but this is not the same as the chain-reaction fission seen in heavy elements.
These are not the same as the controlled fission reactions used in nuclear power or weapons.

3. Practical Impossibility for Chain Reactions

Even if a carbon nucleus were split, it would not produce the conditions necessary for a self-sustaining chain reaction:
- Insufficient neutron production: Fission of carbon nuclei would release very few or no neutrons, meaning it cannot initiate further fission events.
- No energy advantage: The energy required to fission carbon far exceeds any energy released, making it an inefficient and impractical process.

4. What Happens Instead

When carbon nuclei interact with high-energy neutrons, they typically undergo other nuclear processes, such as:
- Neutron capture: Leading to the formation of a heavier isotope, such as $^{13}C$ or $^{14}C$ .
- Spallation: High-energy collisions may cause carbon nuclei to eject smaller particles (like protons or neutrons) rather than splitting into large fragments.

Summary

While it is theoretically possible to fission carbon under extremely high-energy conditions, it is not feasible or practical in any controlled setting like a nuclear reactor. Carbon is highly stable, and its nuclear properties do not support the type of fission used for energy production or weapons.

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