SCIENCE · INVESTIGATE AND EXPLAIN

Audit a nuclear reaction with charge, nucleons and rest energy

Nuclear binding reflects competition between short-range attractive nuclear interactions and proton Coulomb repulsion. A bound nucleus has less rest mass than its separated constituents; the mass difference corresponds to binding energy. Strong binding per nucleon can explain why some light-nucleus fusion and heavy-nucleus fission pathways release energy, but it does not mean every proposed fusion or fission is energetically allowed.

Learning outcome: Compare forward and reverse packets at additional energies 0, 10 and 20 MeV. Retain A, Z, signed Q and the final-energy screen. Contrast the fictional fission packet and state what the energy check cannot establish.

Starting recap

Use scientific notation, signed energy differences and vector momentum. Distinguish a stipulated quantum or nuclear model from actual apparatus and label optional numerical extensions.

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Try

The forward fictional fusion packet has Q=(5.030−5.010)×931.494=18.62988 MeV. Its reverse with 10 MeV additional available energy still has −8.62988 MeV and is forbidden; with 20 MeV, 1.37012 MeV remains for final motion/radiation subject to other conservation laws.

Open the experiment

Predict

Does balancing nucleon number and charge alone prove a reaction can occur spontaneously?

Your prediction and reason

Experiment

Compare forward and reverse packets at additional energies 0, 10 and 20 MeV. Retain A, Z, signed Q and the final-energy screen. Contrast the fictional fission packet and state what the energy check cannot establish.

Audit a stipulated nuclear mass-energy account

Worked teaching model · synthetic values · Original bookkeeping packets, not measured isotope masses: fusion totals 5.030→5.010 u; fission 236.050→235.850 u; reverse fusion 5.010→5.030 u. Additional energy is relative kinetic or compound excitation in the center-of-momentum frame. Accounting does not establish a reaction rate or practical feasibility.

Pattern: 0=fusion, 1=fission, 2=reverse fusion: 0 choice Available center-of-momentum kinetic/excitation energy: 0 MeV

Reset keeps your prediction, captures and practice history.

Stipulated conservation pattern: (A=2,Z=1) + (A=3,Z=1) → (A=4,Z=2) + (A=1,Z=0)

Each plot rescales independently. Compare values and units rather than apparent screen angles. Different panels can represent different quantities and are not silently overlaid.

Calculated evidence ledger — original synthetic model
Quantity	Value	Unit
Initial ground-state rest-mass total	5.03	u
Final ground-state rest-mass total	5.01	u
Q from mass difference	18.63	MeV
Additional available energy	0	MeV
Total incoming nucleons	5	count
Total outgoing nucleons	5	count
Total incoming nuclear charge	2	e
Total outgoing nuclear charge	2	e
Energy budget after final rest masses	18.63	MeV
Meets necessary energy condition	1	flag

The stipulated rest-mass difference and additional energy leave a nonnegative product-energy budget.

These are fictional total nuclear masses for a conservation exercise, not empirical masses or reaction instructions. Nonnegative budget is necessary but not sufficient: momentum, quantum constraints and reaction dynamics still matter. Additional energy is relative kinetic energy or compound excitation in the center-of-momentum frame, not an arbitrary laboratory projectile energy. Mass alone need not be conserved separately; total mass-energy is. Nucleon and charge bookkeeping do not determine a reaction rate.

The stipulated rest-mass difference and additional energy leave a nonnegative product-energy budget.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Begin with evidence

Connect the model

For a specified reaction, Q=(mi−mf)c² compares total initial and final rest masses in one consistent convention. The workbench supplies fictional total nuclear masses, explicitly not empirical isotope data. With mass difference in atomic mass units, use 1 u c²≈931.494 MeV. Positive Q is energy available for final kinetic energy and radiation; negative Q requires an external energy contribution.

Interpret the ledger

The fusion bookkeeping pattern is (A2,Z1)+(A3,Z1)→(A4,Z2)+(A1,Z0). Its supplied totals 5.030 and 5.010 u release 18.62988 MeV. Reversing that same mass packet changes Q’s sign. The separate fission pattern conserves A=236 and Z=92 with fragments (92,36), (141,56) and three neutrons. These balances constrain identity but do not supply a reaction rate or prove a physical isotope is unstable.

Test the boundary

The second control supplies additional available center-of-mass kinetic or excitation energy. A negative total available final energy is forbidden under the stated packet; a nonnegative value is only an energy condition, not a complete probability or momentum analysis. It is not a laboratory projectile threshold formula. No reactor, weapon, fuel preparation, radiation handling or physical nuclear experiment is taught or requested.

Worked original case

Predict, compare and retain evidence

Does balancing nucleon number and charge alone prove a reaction can occur spontaneously? Compare forward and reverse packets at additional energies 0, 10 and 20 MeV. Retain A, Z, signed Q and the final-energy screen. Contrast the fictional fission packet and state what the energy check cannot establish.

Changed-case practice

A fictional nuclear packet has mi−mf=−0.003 u and 4.0 MeV additional center-of-mass energy. Find Q and available final energy; explain the limited conclusion.

Check the reasoning after your attempt

Q=−2.794482 MeV and available final energy=1.205518 MeV. It passes this energy screen, but conservation of momentum and allowed dynamics still matter; no rate or real isotope stability follows.

Apply momentum as a separate nuclear constraint

The short-range strong nuclear interaction binds nucleons despite proton Coulomb repulsion. Fission separates a larger nucleus into smaller products; fusion combines smaller nuclei. A release can be spontaneous or require an initiating energy input, depending on the actual nuclear state and reaction pathway. Conservation balances are necessary, not sufficient rate predictions.

Predict and check: a fictional parent at rest produces two nonrelativistic fragments of masses 3m and m, with no photon or other product in this deliberately restricted packet. Their momenta must be equal and opposite; the lighter fragment has three times the speed and three times the kinetic energy. If 8 MeV is stipulated to become their total kinetic energy, the heavy fragment gets 2 MeV and the light fragment 6 MeV. Splitting the energy equally would violate this packet’s momentum constraint. Adding a photon or a third fragment changes the account, so the two-body result cannot be pasted onto the earlier three-neutron fission pattern. (Current clause 15.7.A.)

Reflect and source-check

Why must atomic and nuclear mass conventions not be mixed without accounting for electrons?

Original prose and supplied numerical evidence; checked 30 October 2026 against the current AP Physics 2 framework, fall 2026 clarifications and OpenStax. Virtual-only: no physical source, exposure or apparatus is requested. Public examples and model captures are not independent mastery or supervised laboratory participation.

Clause-level source/action reconciliation checked 31 October 2026 against the linked current framework and Fall 2026 clarification. Added packets are original virtual comparisons; no new practical or learner-completion claim.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Why must atomic and nuclear mass conventions not be mixed without accounting for electrons?

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Close a two-dimensional photon–electron momentum ledger Next: Track nuclear identity through four decay types

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