22.5.3 Nuclear Fission

Definition

Nuclear fission is the process in which a heavy nucleus (such as ${}_{92}^{235}\text{U}$) absorbs a slow (thermal) neutron and splits into two smaller nuclei of roughly equal mass, releasing a large amount of energy and typically 2–3 neutrons.

${}_{92}^{235}\text{U}{+}_0^{1}n{\to }_{92}^{236}{\text{U}}^{\ast }{\to }_{56}^{141}\text{Ba}{+}_{36}^{92}\text{Kr}+3{}_0^{1}n+Q$

The intermediate nucleus ${}_{92}^{236}{\text{U}}^{\ast }$ is highly unstable and splits almost immediately.

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Why Slow (Thermal) Neutrons?

Fast neutrons are less likely to be captured by ${}_{92}^{235}\text{U}$. Slow (thermal) neutrons have a much higher capture cross-section, meaning they are far more likely to be absorbed and trigger fission. This is why nuclear reactors use a moderator (e.g., water or graphite) to slow neutrons down.

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Binding Energy and Fission

The binding energy per nucleon (B.E./A) curve peaks near iron-56 (~8.8 MeV/nucleon). Heavy nuclei like ${}_{92}^{235}\text{U}$ have a lower B.E./A (~7.6 MeV/nucleon). When they split into medium-mass fragments (e.g., Ba and Kr), the products have a higher B.E./A, meaning the nucleons are more tightly bound. The difference in total binding energy is released as kinetic energy of the fragments.

$\text{Energy released}={\text{B.E.}}_{\text{products}}-{\text{B.E.}}_{\text{reactants}}$

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Energy Released in Fission

The Q-value of a nuclear reaction is the energy released, calculated from the mass difference between reactants and products:

$Q=(m_{\text{reactants}}-m_{\text{products}})c^2$

For the fission of ${}_{92}^{235}\text{U}$, the Q-value is approximately 200 MeV per fission event. This energy appears primarily (~80%) as the kinetic energy of the fission fragments, with the remainder as kinetic energy of neutrons, gamma radiation, and energy from subsequent beta decays.

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Fission Energy vs. Chemical Energy

A single fission event releases ~$200\text{ MeV}$. A typical chemical reaction (e.g., burning one molecule of fuel) releases only ~$10\text{ eV}$. This means:

$\frac{200\text{ MeV}}{10\text{ eV}}=\frac{200\times 10^6\text{ eV}}{10\text{ eV}}=2\times 10^7$

Nuclear fission releases approximately 20 million times more energy per event than a chemical reaction. This is because fission converts a small amount of mass directly into energy via $E=\Delta m{c}^2$, whereas chemical reactions only rearrange electrons.

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Chain Reaction

Each fission event releases on average 2–3 neutrons. These neutrons can trigger further fission events in neighbouring ${}_{92}^{235}\text{U}$ nuclei, leading to a chain reaction — a self-sustaining series of fission events.

• Uncontrolled chain reaction → exponential energy release → nuclear weapon
• Controlled chain reaction → steady power output → nuclear reactor

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Critical Mass

For a chain reaction to be self-sustaining, the fissile material must exceed a minimum amount called the critical mass. Below this mass, too many neutrons escape the material without causing further fission, and the reaction dies out (sub-critical). Above critical mass, the reaction grows exponentially (super-critical).

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Fission Products

The fission of ${}_{92}^{235}\text{U}$ does not always produce the same fragments. Common products include: