Nuclear reactions, fission, and fusion
Calculate binding, reaction energy, rates, and the difference between nuclear events and useful power.
Advance from isotope language to reaction equations, Q-values, cross sections, chain reactions, plasma fusion, and lattice-assisted experiments.
Before you begin
- • Level 1 atoms and radiation
- • Mechanics and energy conservation
- • Basic exponential reasoning
By the end, you can
- • Balance charge and nucleon number in reactions.
- • Calculate reaction Q-values from mass differences.
- • Explain fission chains and fusion barriers.
- • Separate detected products, reaction yield, thermal output, and net power.
Interactive model
Explore before calculating
Live laboratory
Counts-to-yield ladder
Separate a detector excess from inferred reactions and from useful power. Every rung adds an assumption that must be calibrated.
Net excess: 300 counts
Simple significance: 11.34σ
Inferred reactions: 6.00e+4
Inferred power: 6.41e-10 W
This conversion assumes equal background exposure, one declared emission branch, and calibrated efficiency and acceptance. Even a strong count excess does not establish net heat or electrical output.
Level 2 · Secondary physics teaching kit
Record the investigation. Teach the reasoning.
A learner-facing lab record and a course-specific instructor guide turn the live model into a repeatable classroom investigation.
Learner record
Reaction yield and detector-efficiency audit
How do beam rate, target thickness, cross section, and detection efficiency combine into an expected count rate?
Download learner recordInstructor guide
Teach for evidence, not button pushing
Learners construct a reaction-yield ledger and separate modeled physical events from detector acceptance, backgrounds, and identification.
Download instructor guideLesson 1 of 3
Reaction equations and Q-values
Which conserved quantities identify a possible nuclear reaction and its energy release?
Nuclear equations conserve electric charge, nucleon number, total energy, momentum, and angular momentum. Rest-mass difference appears as kinetic energy or radiation.
The Q-value is initial rest energy minus final rest energy. Positive Q means energy is released, though a reaction may still face an activation or Coulomb barrier.
Worked example
Products have 0.005 u less mass than reactants. Estimate released energy using 931.5 MeV/u.
- 1. Use Q = Δm c².
- 2. Multiply 0.005×931.5 MeV.
- 3. Keep significant figures.
Q ≈ 4.66 MeV per reaction.
Try it
Balance reaction cards
Materials: Cards labeled p, n, deuteron, alpha, electron, photon.
- 1. Choose reactant cards.
- 2. Propose products.
- 3. Count charge and nucleon number on both sides.
- 4. Reject channels that fail conservation before discussing likelihood.
Notice: Conservation narrows possibilities but does not determine reaction probability.
Check your understanding: Does positive Q guarantee a reaction occurs rapidly at room temperature?
Answer: No.
Kinetic barriers, selection rules, and tiny cross sections can suppress energetically allowed reactions.
Lesson 2 of 3
Fission chains and fusion barriers
Why can both splitting heavy nuclei and joining light nuclei release energy?
Binding energy per nucleon rises toward the iron region. Heavy-nucleus fission and light-nucleus fusion can both move products toward tighter binding.
Fission can multiply neutrons into a chain reaction. Fusion requires sufficient collision energy and confinement to overcome repulsion and achieve useful reaction probability.
Worked example
A fusion plasma has 10 MW heating input and 15 MW fusion output. What is Q_plasma?
- 1. Define Q = fusion power/heating power.
- 2. Compute 15/10.
- 3. Do not confuse plasma Q with electrical plant net power.
Q_plasma = 1.5; total facility power and conversion losses still determine net electricity.
Try it
Chain-reaction probability model
Materials: Dice and a branching worksheet.
- 1. Let each neutron produce two successors only on selected die outcomes.
- 2. Run subcritical and supercritical probability rules.
- 3. Plot generation size.
- 4. Relate probability to multiplication factor.
Notice: Small changes in average reproduction determine whether a chain dies out or grows.
Check your understanding: Why is plasma fusion power not identical to grid electricity?
Answer: Heating, magnets, pumps, conversion, and facility loads must also be counted.
Net plant power uses a larger system boundary than fusion power inside the plasma.
Lesson 3 of 3
Reaction rates, detectors, and net power
How do a few nuclear products scale—or fail to scale—into a useful energy source?
Reaction rate depends on particle density, cross section, relative speed, geometry, and time. Detector efficiency converts actual emissions into observed counts.
A statistically significant nuclear signature can establish reactions without establishing useful heat. Calorimetry, backgrounds, chemical controls, and complete electrical input are separate evidence lines.
Worked example
A detector with 10% efficiency records 500 source counts above background.
- 1. Efficiency = detected/incident.
- 2. Estimate incident events as 500/0.10.
- 3. State geometry assumptions.
About 5000 emissions reached the detector's acceptance; total reactions may be larger depending on solid angle and branching.
Try it
Counts-to-power ladder
Materials: A hypothetical count dataset and calculator.
- 1. Subtract background with uncertainty.
- 2. Correct for detector efficiency and geometry.
- 3. Convert inferred reactions to energy using Q-value.
- 4. Compare with measured heat and input power.
Notice: Each conversion adds assumptions; a signal can be nuclear yet energetically negligible.
Check your understanding: What extra measurement is needed before neutron counts support a net-energy claim?
Answer: A calibrated full-system energy balance, usually including calorimetry and all inputs.
Counts establish particles, not automatically total useful energy.
Formula-to-meaning deck
Read the equation in ordinary language.
Q = (m_initial − m_final)c²
Reaction mass difference becomes released or absorbed energy.
Units: J or MeV
R ∝ n₁n₂⟨σv⟩
Fusion reaction rate depends on densities and velocity-averaged cross section.
Units: reactions/(m³·s)
N_detected = εN_incident
Detector efficiency links incident particles to recorded counts.
Units: counts
Independent practice
Problem set
Work each problem before opening its hint and solution.
1. A mass defect is 0.0020 u. Estimate Q in MeV.
Reveal hint
Multiply by 931.5 MeV/u.
Reveal solution
About 1.86 MeV.
2. A 5% efficient detector records 200 net counts. Estimate incident particles in its acceptance.
Reveal hint
Divide by 0.05.
Reveal solution
4000 particles.
3. A system outputs 120 W heat with 150 W electrical input. What is measured net power?
Reveal hint
Output minus input for the stated boundary.
Reveal solution
−30 W; it consumes net power.
Continue into the evidence