Separate binding energy, reaction energy and channel feasibility
An abstract reaction ledger has initial nuclei labeled (A,Z)=(12,6) and (4,2), with final labels (15,7) and (1,1). Both sides total A=16 and Z=8. These fictional labels are an inventory exercise, not evidence that a particular reaction occurs or has an appreciable cross section. Nuclear rest masses are used consistently; electron masses are not silently mixed into the sum.
Learning outcome: Balance A and Z before computing Q. Compare positive and negative mass differences, identify the center-of-momentum threshold and withhold product partitions in forbidden cases. Then compute the separate binding ledger and explain why its reference state differs.
Starting recap
Review finite sums, exponential and logarithmic functions, radial integration measures, first-order coupled equations and mass-energy units. Keep state counts, occupations, calibration records and unused tests distinct.
All lessons are open directly. Your saved experiments remain when you leave and return.
Try
For reaction mass difference +0.005 u, Q=4.6575 MeV. With incoming center-of-momentum kinetic energy5 MeV, final total is9.6575 MeV. The approximate heavy and light shares are0.60359375 and9.05390625 MeV. Changing Q to−9.315 MeV while retaining5 MeV incoming rejects the channel rather than yielding negative product energies.
Open the experimentPredict
What must happen when Q plus incoming center-of-momentum kinetic energy is negative?
Experiment
Balance A and Z before computing Q. Compare positive and negative mass differences, identify the center-of-momentum threshold and withhold product partitions in forbidden cases. Then compute the separate binding ledger and explain why its reference state differs.
Close inventory before interpreting a reaction energy
Worked teaching model · synthetic values · Fictional nuclear ledger (A, Z)=(12, 6)+(4, 2) to (15, 7)+(1, 1), all nuclear masses with no electron bookkeeping. Supplied total rest-mass difference gives Q using931.5 MeV/u. Two-body nonrelativistic final energy partition uses approximate inertial mass ratio 15:1. Negative total available kinetic energy rejects this channel; no actual isotope, reaction rate or material operation is implied.
Reset keeps your prediction, captures and practice history.
Channel energy threshold in center-of-momentum frame
Graph axes rescale independently; read units and values, not screen angles. 1: Q plus incoming kinetic energy (solid). Joined curves show the supplied model, not additional observations.
Equivalent numerical coordinates for Channel energy threshold in center-of-momentum frame
Q plus incoming kinetic energy
| incoming kinetic energy (MeV) | available final kinetic energy (MeV) |
|---|---|
| 0 | 4.6575 |
| 0.1666667 | 4.824167 |
| 0.3333333 | 4.990833 |
| 0.5 | 5.1575 |
| 0.6666667 | 5.324167 |
| 0.8333333 | 5.490833 |
| 1 | 5.6575 |
| 1.166667 | 5.824167 |
| 1.333333 | 5.990833 |
| 1.5 | 6.1575 |
| 1.666667 | 6.324167 |
| 1.833333 | 6.490833 |
| 2 | 6.6575 |
| 2.166667 | 6.824167 |
| 2.333333 | 6.990833 |
| 2.5 | 7.1575 |
| 2.666667 | 7.324167 |
| 2.833333 | 7.490833 |
| 3 | 7.6575 |
| 3.166667 | 7.824167 |
| 3.333333 | 7.990833 |
| 3.5 | 8.1575 |
| 3.666667 | 8.324167 |
| 3.833333 | 8.490833 |
| 4 | 8.6575 |
| 4.166667 | 8.824167 |
| 4.333333 | 8.990833 |
| 4.5 | 9.1575 |
| 4.666667 | 9.324167 |
| 4.833333 | 9.490833 |
| 5 | 9.6575 |
| 5.166667 | 9.824167 |
| 5.333333 | 9.990833 |
| 5.5 | 10.1575 |
| 5.666667 | 10.32417 |
| 5.833333 | 10.49083 |
| 6 | 10.6575 |
| 6.166667 | 10.82417 |
| 6.333333 | 10.99083 |
| 6.5 | 11.1575 |
| 6.666667 | 11.32417 |
| 6.833333 | 11.49083 |
| 7 | 11.6575 |
| 7.166667 | 11.82417 |
| 7.333333 | 11.99083 |
| 7.5 | 12.1575 |
| 7.666667 | 12.32417 |
| 7.833333 | 12.49083 |
| 8 | 12.6575 |
| 8.166667 | 12.82417 |
| 8.333333 | 12.99083 |
| 8.5 | 13.1575 |
| 8.666667 | 13.32417 |
| 8.833333 | 13.49083 |
| 9 | 13.6575 |
| 9.166667 | 13.82417 |
| 9.333333 | 13.99083 |
| 9.5 | 14.1575 |
| 9.666667 | 14.32417 |
| 9.833333 | 14.49083 |
| 10 | 14.6575 |
At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.
| Quantity | Value | Unit |
|---|---|---|
| Nucleon number initial minus final | 0 | integer |
| Charge number initial minus final | 0 | integer |
| Reaction Q value | 4.6575 | MeV |
| Available final center-of-momentum kinetic energy | 9.6575 | MeV |
| Energetically allowed under stated channel | 1 | flag |
| Approximate heavy-product kinetic energy | 0.6035937 | MeV |
| Approximate light-product kinetic energy | 9.053906 | MeV |
| Separate fictional A 16 nuclear binding mass defect | 0.147528 | u |
| Separate fictional A 16 binding energy | 137.4223 | MeV |
Inventory and energy allow this abstract channel; neither establishes a nonzero reaction probability.
Conserve A and Z:16=16 and8=8. Q=(sum initial nuclear masses−sum final nuclear masses)c². In the center-of-momentum frame final momenta are opposite; in the supplied nonrelativistic15:1 mass-ratio approximation, the lighter product receives15/16 of the available kinetic energy. This is not a laboratory projectile-threshold formula. Binding energy compares a separate nucleus with free nucleons, not with arbitrary reaction products.
Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.
Inventory and energy allow this abstract channel; neither establishes a nonzero reaction probability.
Conserve A and Z:16=16 and8=8. Q=(sum initial nuclear masses−sum final nuclear masses)c². In the center-of-momentum frame final momenta are opposite; in the supplied nonrelativistic15:1 mass-ratio approximation, the lighter product receives15/16 of the available kinetic energy. This is not a laboratory projectile-threshold formula. Binding energy compares a separate nucleus with free nucleons, not with arbitrary reaction products.
Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.
Understand
Apply
Public practice checks a specific claim. It does not establish independent mastery.
Which independent calibration, state-counting or physical-domain premise is needed, and which fresh observation could challenge the inference?
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.
Save a science backup or import one
Science work is stored locally in this browser, separately from mathematics and AI. It does not sync automatically. Use this science-only backup; this checkout's older all-subject export does not include science.
A legacy file is available only when the complete snapshot fits the 36 MB limit. For larger snapshots, prepare a complete file set below; never discard notebooks to make a smaller file.
Matching imported notebook drafts replace their current drafts. Omitted lessons and known first attempts remain. Export your current work first if you want to retain both drafts.
Complete file sets and course backups
A file set can hold more work than one science file. Keep its manifest and every part together. Each file is limited to 36 MB. This format needs this version of LearnAI or a compatible newer version; older versions can use only the legacy single-file backup above.
The set includes every saved science course and global continuation at this moment. Later edits need a new export. A conflicting tab exports its own visible work, which may differ from saved work in another tab.
0 file(s) selected. File order and filenames do not determine identity. Missing, changed or conflicting parts block the entire restore; no good part is applied by itself.
Science storage: loading. No account or remote computation is required.