Nuclear Fission
Contents
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 (
) absorbing a neutron (
) and splitting:
![\[{}^{235}_{92}U + n \rightarrow {}^{141}_{56}Ba + {}^{92}_{36}Kr + 3n + \text{Energy}\]](http://latex.artofproblemsolving.com/2/a/0/2a03797c3979c8b5c2ccc036e929d87fff5752c9.png)
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:
![\[E = \Delta m \cdot c^2,\]](http://latex.artofproblemsolving.com/a/2/d/a2db081a1bf14c51df344c557db31c65d0120509.png)
where 
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 
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
must satisfy 
, 
means critical (steady state),
means supercritical (reaction grows exponentially),
means subcritical (reaction dies out).
,
means critical (steady state),
means supercritical (reaction grows exponentially),
means subcritical (reaction dies out).Controlling 
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.,
, 
), - 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 ,
- 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:
![\[{}^{235}_{92}U + n \rightarrow \text{Fission fragments} + 2-3n + 200\ \text{MeV}\]](http://latex.artofproblemsolving.com/7/e/c/7eca38305f3e819b0bbb5334d039a7e29105b325.png)
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 |  |
|
| Applications | Stars, experimental reactors, hydrogen bombs | Nuclear power plants, atomic bombs |
Example Calculation
If 1 kg of 
undergoes complete fission:
- Number of nuclei in 1 kg:
![\[N = \frac{1000\ \text{g}}{235\ \text{g/mol}} \times 6.022 \times 10^{23} \approx 2.56 \times 10^{24}\]](http://latex.artofproblemsolving.com/a/d/5/ad59faa56a41f9ba24f1d237093158c51f32e7a3.png)
- Total energy released:
![\[E = N \times 200\ \text{MeV} \times 1.6 \times 10^{-13}\ \text{J/MeV} \approx 8.2 \times 10^{13}\ \text{J}\]](http://latex.artofproblemsolving.com/c/d/6/cd616c632caac514e0a2f6608fe3974b0cd2b243.png)
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.
