Nuclear Fission

Nuclear fission is a nuclear reaction in which a heavy atomic nucleus splits into two (or more) lighter nuclei, along with the release of a large amount of energy, neutrons, and gamma radiation. Fission is the principle behind nuclear reactors and atomic bombs.

The Fission Process

A common fission reaction involves uranium-235 ( ${}^{235}_{92}U$ ) absorbing a neutron ( $n$ ) and splitting:

${}^{235}_{92}U + n \rightarrow {}^{141}_{56}Ba + {}^{92}_{36}Kr + 3n + \text{Energy}$

This means:

A uranium nucleus captures a neutron,
It becomes unstable and splits into barium-141, krypton-92, and releases 3 neutrons,
A large amount of energy (approximately 200 MeV) is released.

Energy from Fission

The energy released comes from the difference in binding energy before and after the fission reaction. Using Einstein’s mass-energy equivalence:

$E = \Delta m \cdot c^2,$

where $\Delta m$ is the mass defect (difference between mass of original nucleus plus neutron and total mass of fission products).

Typical energy release per fission is about 200 MeV, which is about $3.2 \times 10^{-11}$ joules.

Chain Reactions

The 3 neutrons released can induce fission in other uranium nuclei, creating a chain reaction.

For a sustained chain reaction:

The multiplication factor $k$ must satisfy $k \geq 1$ ,
$k = 1$ means critical (steady state),
$k > 1$ means supercritical (reaction grows exponentially),
$k < 1$ means subcritical (reaction dies out).

Controlling $k$ is essential in nuclear reactors.

Critical Mass

The minimum amount of fissile material required to sustain a chain reaction is called the critical mass. It depends on:

Material type (e.g., ${}^{235}U$ , ${}^{239}Pu$ ),
Shape and density,
Presence of neutron reflectors.

Fission Products and Radioactivity

Fission fragments are highly radioactive isotopes, causing:

Radioactive decay chains,
Release of beta and gamma radiation,
Nuclear waste challenges.

Nuclear Reactors

Reactors control the fission chain reaction to produce heat:

Neutron moderators slow down neutrons to increase fission probability,
Control rods absorb neutrons to regulate $k$ ,
Heat generated turns water into steam to drive turbines.

Nuclear Weapons

Atomic bombs use uncontrolled chain reactions with:

Rapid assembly of a supercritical mass,
Explosion energy on the order of kilotons to megatons of TNT equivalent.

Example reaction for bomb-grade uranium:

${}^{235}_{92}U + n \rightarrow \text{Fission fragments} + 2-3n + 200\ \text{MeV}$

Fusion vs. Fission

Aspect	Fusion	Fission
Fuel	Light elements (e.g. H, He)	Heavy elements (e.g. U-235, Pu-239)
Waste	Minimal	Long-lived radioactive byproducts
Energy per kg	Higher than fission	Lower than fusion
Conditions needed	Extremely high temperature and pressure	Neutron flux and critical mass
Natural occurrence	Stars (like the Sun)	None (rare natural decays only)
Example reaction	${}^2_1\text{H} + {}^3_1\text{H} \rightarrow {}^4_2\text{He} + n + 17.6\ \text{MeV}$	${}^{235}_{92}\text{U} + n \rightarrow {}^{141}_{56}\text{Ba} + {}^{92}_{36}\text{Kr} + 3n + 200\ \text{MeV}$
Applications	Stars, experimental reactors, hydrogen bombs	Nuclear power plants, atomic bombs

Example Calculation

If 1 kg of ${}^{235}U$ undergoes complete fission:

Number of nuclei in 1 kg:

$N = \frac{1000\ \text{g}}{235\ \text{g/mol}} \times 6.022 \times 10^{23} \approx 2.56 \times 10^{24}$

Total energy released:

$E = N \times 200\ \text{MeV} \times 1.6 \times 10^{-13}\ \text{J/MeV} \approx 8.2 \times 10^{13}\ \text{J}$

This equals about 20 kilotons of TNT (the energy released by the bomb dropped on Hiroshima).

Safety and Waste Disposal

Nuclear fission produces radioactive waste requiring:

Shielding and cooling,
Long-term storage,
Potential reprocessing and recycling.

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Nuclear Fission

Contents

Nuclear Fission

The Fission Process

Energy from Fission

Chain Reactions

Critical Mass

Fission Products and Radioactivity

Nuclear Reactors

Nuclear Weapons

Fusion vs. Fission

Example Calculation

Safety and Waste Disposal

See Also