23.1.5Quantum and nuclear physics (A Level)
Calculating Energy Released in Nuclear Reactions
5 min read 9 parts Lesson 18 of 23 1 quiz
Lesson summary
23.1.5 Calculating Energy Released in Nuclear Reactions — AS PHYSICS 9702 notes: Calculate the energy released in nuclear reactions from mass change or from binding energies, and describe how the energy is shared.Binding energy released — E = (Δm)c2, where Δm is the mass defect a…
- Daughter nuclei
- Mass method
- Binding-energy method
- Electron masses
- Free nucleons
- Reason for fusion and fission
Section 1 of 9Source of the energy released
Binding energy released
- E = (Δm)c2, where Δm is the mass defect and c the speed of light.
Daughter nuclei
- Both fission and fusion products have a higher binding energy per nucleon than the parent nuclei.
Energy
- The released energy comes from the mass difference between parent and daughter nuclei.
Section 2 of 9Two equivalent methods
Mass method
- Q = c2.
- (total mass of reactants − total mass of products)
- A positive answer means energy is released.
Binding-energy method
- Q = − (total binding energy of reactants).
- (total binding energy of products)
- A rise in total binding energy means energy is released.
Choice
- Use the mass method when masses are given and the binding-energy method when binding energies per nucleon are supplied.
Section 3 of 9Mass method steps
1
Write the balanced equation so that all products, including neutrons or photons, are included.
2
Add the rest masses of all particles on each side in u, using nuclear or atomic masses consistently.
3
Find Δm = mreactants − mproducts.
4
Convert using Q = Δm × 931.5 MeV u−1, or Δm in kg × c2 for joules.
- Electron masses
- With atomic masses, electrons balance automatically in alpha decay, fission and β− decay.
- For β+ decay use nuclear masses or subtract two electron masses.
Section 4 of 9Binding-energy method steps
1
Multiply the binding energy per nucleon by the nucleon number to get each nuclide's total.
2
Add the totals for the products and for the reactants.
3
Subtract the reactant total from the product total.
1Free nucleons
- They have zero binding energy, so free neutrons add nothing to the sum.
2Direction
- Products minus reactants gives a positive number when energy is released.
3Reason for fusion and fission
- Both changes raise the total binding energy.
4Favoured reaction
- A reaction releasing more energy produces more stable products and is more likely.
Section 5 of 9Where the energy goes
Kinetic energy
- The released energy appears as kinetic energy of the products and sometimes as a gamma photon.
Momentum
- In decay of a stationary nucleus into two bodies, the products move in opposite directions with equal momentum.
Sharing
- Kinetic energy is p2/2m, so the lighter product receives the larger share.
Alpha decay
- The alpha particle takes about 98% of the kinetic energy, so alpha energies are well defined and can identify the nuclide.
Fission fragments
- The lighter fragment moves faster and carries more kinetic energy.
- The rest of the roughly 200 MeV is carried by neutrons, gamma-rays and later beta and gamma radiation.
Thermal energy
- In a reactor all of it ends up as thermal energy, so cooling is essential after shutdown.
Section 6 of 9Typical values for checking
| Process | Energy released |
|---|---|
| Fission of one uranium-235 nucleus | about 200 MeV |
| Deuterium-tritium fusion | 17.6 MeV |
| Alpha decay of heavy elements | 4 to 6 MeV |
| Chemical reaction per atom | a few eV |
Section 7 of 9More from the specification
More from the specification
Nuclear mass defect and electrostatic forces
- Nuclear mass defect and electrostatic forces mass converted into nuclear binding energy overcomes repulsive electrostatic forces between adjacent positively charged nucleons.
Mass-energy equivalence
- The principle that mass and energy are interchangeable, E = mc2.
Electrostatic force
- Force between charged objects, attractive or repulsive
Proton
- Positive particle in the nucleus, relative charge +1 and relative mass 1.
Helium
- Product of the fusion of hydrogen in stars.
Force
- A push or pull measured in newtons.
Electrostatic
- Relating to electric charges that are stationary.
Gradient
- Slope of a graph line.
E = mc2
What the symbols mean: E = energy (J) · m or Δm = mass (change) (kg) · c = 3.00 × 108 m s−1
Section 8 of 9Key terms
| Term | Meaning |
|---|---|
| Q value | The energy released in a nuclear reaction. |
| Mass defect | The difference between the mass of separate nucleons and the nucleus. |
| Binding energy | The energy required to separate a nucleus into its protons and neutrons. |
| Unified atomic mass unit | One twelfth of the mass of a carbon-12 atom, equivalent to 931.5 MeV. |
| Daughter nucleus | The nucleus produced by a nuclear decay or reaction. |
Section 9 of 9Exam technique
1
Subtracting reactant mass from product mass and quoting a negative energy as energy released — check the direction of subtraction.
2
Forgetting to include all particles such as the neutron in the product mass — include every product.
3
Applying 931.5 MeV per u to masses in kg — it applies only to masses in u.
4
Forgetting that a lighter product carries away more kinetic energy — momentum is shared equally and opposite.
5
Using binding energy per nucleon instead of total binding energy in the sum — multiply by the nucleon number first.