Fission (AQA A-Level Physics): Revision Notes
Fission
What is fission?
Fission is a nuclear process in which a heavy nucleus splits into two lighter nuclei. Analysis of the binding energy per nucleon curve reveals that fission can serve as a source of energy. When we examine a very heavy nucleus positioned at the far right of the binding energy curve, we find that splitting it into lighter nuclei (while still maintaining nucleon numbers greater than 56) leads to an interesting result.
The products of fission have higher binding energy per nucleon compared to the original heavy nucleus. This means the total binding energy of the system increases during fission. Since binding energy represents how tightly the nucleus is held together, an increase in binding energy corresponds to a more stable configuration. This increase in binding energy results in a decrease in the total mass of the system - a mass defect. According to Einstein's mass-energy equivalence principle, this lost mass is converted into energy that transfers to the surroundings.
The binding energy per nucleon curve is crucial for understanding why fission releases energy. Heavy nuclei at the right end of the curve have lower binding energy per nucleon than medium-sized nuclei. When fission occurs, the products move toward the peak of the curve, gaining binding energy and releasing the difference as usable energy.
Spontaneous fission
Spontaneous fission is a very rare natural process in which certain heavy nuclei undergo fission without any external trigger. Although uncommon, spontaneous fission can occur in nuclei such as uranium-235.
Example: Uranium-235 spontaneous fission
A uranium-235 nucleus can spontaneously split into two lighter nuclei. One possible fission reaction produces strontium-90 and xenon-143, along with two neutrons:
The energy released during this fission event can be calculated using two different methods, both of which should give approximately the same result.
Calculating energy release using binding energy per nucleon
Worked Example: Energy from Binding Energy per Nucleon
The first method involves calculating the change in total binding energy of the system. We need the binding energy per nucleon values for each nucleus involved:
- Uranium-235: 7.59 MeV/nucleon
- Strontium-90: 8.70 MeV/nucleon
- Xenon-143: 8.20 MeV/nucleon
The change in binding energy represents the energy released to the surroundings. We calculate this by finding the total binding energy before and after the fission:
Step 1: Calculate initial total binding energy
Step 2: Calculate final total binding energy
Step 3: Calculate the change in binding energy
This positive change indicates that the products are more tightly bound than the original nucleus, and approximately 172 MeV of energy is released to the surroundings.
Calculating energy release using mass loss
The second method involves calculating the actual decrease in mass during the fission process and converting this mass defect into energy using Einstein's equation .
The atomic mass unit (u) is defined as 1/12 the mass of a carbon-12 atom. When working with atomic mass units, we can use the conversion factor: , or simply 1 u is equivalent to 931.5 MeV when converted to energy.
Worked Example: Energy from Mass Loss
For this calculation, we need the masses of each particle involved:
- Uranium-235 nucleus: 234.99342 u
- Strontium-90 nucleus: 89.88688 u
- Xenon-143 nucleus: 142.90525 u
- Neutron: 1.00867 u
Step 1: Calculate total mass before fission
Step 2: Calculate total mass after fission
Step 3: Calculate mass loss
Step 4: Convert mass defect to energy
This result agrees closely with the binding energy method (172 MeV), with the small difference due to rounding in the binding energy per nucleon values.
Remember!
Key Points to Remember:
- Fission splits heavy nuclei into two medium-sized nuclei with nucleon numbers still greater than 56, releasing energy because the products have higher binding energy per nucleon.
- Two methods calculate fission energy: either by finding the increase in total binding energy, or by calculating the mass defect and using with the conversion .