GENERAL CHEMISTRY · NUCLEAR REACTIONS STUDY MAP

Conserve the nucleus.
Name the change.

Move through fifteen source-mapped outcomes covering nuclide equations, binding energy, radioactive decay, nuclear particles, and precise terminology—without blurring nuclear and chemical models.

Start the lessons →Build a balanced mix ↗Explore all objectives ↓
5guided lessons
15bounded objectives
20practice questions
0invented topic weights

Scope boundary

A nuclear equation closes two ledgers.

The ADA names Balancing equations, Binding energy, Decay processes, Particles, and Terminology. It does not publish topic-level weights or question quotas, so these DAT TRAIN outcomes organize study without pretending to predict a test form.

Nuclear Reactions owns nuclide notation, mass-number and atomic-number conservation, mass defect, binding energy, decay, nuclear particles, radiation quantities, and nuclear terminology. Atomic and Molecular Structure owns electronic configurations and ordinary ion inventories; Thermodynamics owns the broader energy framework. Chemical Kinetics owns empirical chemical rate laws, while this domain applies first-order mathematics to nuclear decay.

Nuclear decision sequence

Four checks before trusting a nuclear claim.

  1. 01

    Inventory

    Name every nuclide and particle, record A and Z, separate ionic charge, and identify the sample quantity and requested basis.

  2. 02

    Conservation

    Sum mass numbers and atomic numbers independently, then solve the missing particle or nuclide without importing ordinary chemical atom rules.

  3. 03

    Model

    Choose total or per-nucleon binding energy, the decay law, a radiation comparison, or fission/fusion/transmutation terminology from the evidence.

  4. 04

    Units and limits

    Keep atomic and nuclear masses consistent; track u, kg, J, eV, MeV, time, Bq, Ci, Gy, and Sv; use only supplied constants and conditions.

Official hierarchy → learning sequence

Five branches. Fifteen outcomes.

Open a topic to inspect its observable outcomes, model boundaries, prerequisite graph, misconception corrections, representations, and direct free references. Then use the 5 lessons or balanced practice to retrieve the same frozen objective set.

ABalancing equations3 objectives
Objective 1GC-NUC-BAL-01

Nuclide notation and particle inventory

Read and write nuclide notation and determine a species’ proton, neutron, and electron inventory from mass number, atomic number, and any separately stated ionic charge.

Must know
In nuclide notation, A is written above Z to the left of X; A is the number of nucleons, Z is the number of protons, and the neutron count is A − Z. For a neutral atom the electron count equals Z; an ionic charge changes the electron inventory but does not change A, Z, or element identity.
Model boundary
Treat mass number as an integer nucleon count, not as average atomic mass. Use isotope masses, abundances, or electron-binding corrections only when the prompt supplies them or explicitly requires them.
Misconception
The periodic-table atomic mass should be placed in the upper-left position of every nuclide symbol. The upper-left value is the integer mass number of one nuclide; periodic-table atomic mass is generally an abundance-weighted average.
Earlier objectives in this map
None
Objective 2GC-NUC-BAL-02

Mass-number and atomic-number conservation

Balance a supplied nuclear equation or identify a missing nuclide or particle by conserving total mass number and total atomic number independently.

Must know
The sum of upper-left mass numbers and the sum of lower-left atomic numbers must each match across a nuclear equation. A nuclide’s Z identifies its element, while a separately written ionic charge belongs to an electron inventory and cannot replace the lower-left nuclear ledger.
Model boundary
Balance the particles and nuclides named by the prompt. Do not impose ordinary chemical atom conservation on a transmutation or add unrequested particles merely to force a preferred decay story.
Misconception
A nuclear equation is balanced when the chemical element symbols are unchanged on both sides. Nuclear reactions may change element identity; balance the independent A and Z totals and use the resulting Z to identify each nuclide.
Earlier objectives in this map
Nuclide notation and particle inventory
Objective 3GC-NUC-BAL-03

Decay and bombardment equations

Construct and verify alpha, beta-minus, positron, electron-capture, gamma, neutron-bombardment, or proton-bombardment equations when the process and required participants are supplied.

Must know
Common introductory particles carry ledger pairs α = ⁴₂He, β⁻ = ⁰₋₁e, β⁺ = ⁰₊₁e, γ = ⁰₀γ, neutron = ¹₀n, and proton = ¹₁p. Every final equation must close both A and Z, place a captured particle on the reactant side and an emitted particle on the product side, and preserve the stated reaction direction.
Model boundary
Include neutrinos, antineutrinos, excited-state symbols, or multi-step intermediates only when the prompt or supplied convention includes them; the introductory A/Z ledger alone does not determine a mechanism.
Misconception
Beta-minus emission lowers atomic number because a negatively charged particle leaves the nucleus. In beta-minus decay a neutron converts to a proton as the electron is emitted, so A is unchanged and the daughter Z increases by one.
Earlier objectives in this map
Mass-number and atomic-number conservation
BBinding energy3 objectives
Objective 1GC-NUC-BIN-01

Mass defect from supplied masses

Calculate a nucleus or atom’s mass defect from a supplied, internally consistent nuclear-mass or atomic-mass convention and a complete free-particle inventory.

Must know
With nuclear masses, Δm = Zmₚ + (A − Z)mₙ − m_nucleus; with neutral atomic masses, the common introductory shortcut uses Z hydrogen-atom masses plus neutron masses minus the neutral-atom mass. The free and bound inventories must contain the same protons, neutrons, and electrons under the chosen convention; mixing a bare-proton mass with a neutral-atom mass silently breaks that inventory.
Model boundary
Use the mass values and electron convention supplied. Neglect electron binding energy or other small corrections only when the stated data model permits it, and do not substitute a rounded periodic-table average for a nuclide mass.
Misconception
Mass defect is found by subtracting the separate nucleon masses from the bound nuclide mass, regardless of which atomic or nuclear masses are listed. Use free-particle mass minus bound-system mass and keep the electron inventory consistent with the supplied mass convention.
Earlier objectives in this map
Nuclide notation and particle inventory
Objective 2GC-NUC-BIN-02

Binding energy and energy units

Convert a mass defect to total binding energy with E = Δmc² or a supplied mass–energy equivalence and report the result in the requested joule, electron-volt, or megaelectron-volt unit.

Must know
When Δm is in kilograms, E = Δmc² gives joules; when Δm is in atomic mass units, a supplied equivalence such as 1 u·c² ≈ 931.5 MeV can give nuclear-scale energy directly. The magnitude depends on whether the question asks for one nucleus, one mole of nuclei, the entire sample, or energy per nucleon, so the requested basis is part of the unit ledger.
Model boundary
Use supplied constants and stated precision. Do not mix u, kg, J, eV, MeV, particle, and mole bases without an explicit conversion, and do not interpret binding energy as a chemical bond enthalpy.
Misconception
A mass defect stated in atomic mass units can be inserted directly into E = mc² with c in meters per second to obtain joules. Convert the mass to kilograms first or use a compatible supplied u-to-energy equivalence.
Earlier objectives in this map
Mass defect from supplied masses
Objective 3GC-NUC-BIN-03

Binding energy per nucleon and stability

Calculate binding energy per nucleon and use it with supplied stability evidence to compare how tightly nuclei are bound without confusing it with total binding energy or decay rate.

Must know
Binding energy per nucleon equals total binding energy divided by A; among otherwise comparable nuclei, a larger value indicates more energy would be required per nucleon to separate the nucleus. Total binding energy generally grows with nucleus size, so total energy alone is not the normalized comparison; nuclear stability and decay mode also depend on proton–neutron balance and permitted transformations.
Model boundary
Use supplied binding energies, masses, graphs, or stated stability patterns. Do not infer an exact half-life, unique decay path, or reaction yield from binding energy per nucleon alone.
Misconception
The nucleus with the largest total binding energy must be the most tightly bound and therefore can never decay. Compare energy per nucleon for tightness, and treat stability and decay as additional evidence-dependent questions.
Earlier objectives in this map
Binding energy and energy units
CDecay processes3 objectives
Objective 1GC-NUC-DEC-01

Parent–daughter changes by decay mode

Predict the daughter mass number and atomic number for a stated alpha, beta-minus, positron, electron-capture, or gamma decay and identify the daughter element.

Must know
Alpha decay changes A by −4 and Z by −2; beta-minus leaves A unchanged and changes Z by +1; positron emission and electron capture leave A unchanged and change Z by −1. Gamma emission changes neither A nor Z because it represents nuclear de-excitation; parent and daughter labels refer to the nuclide before and after the stated transformation.
Model boundary
Predict the daughter from a stated decay mode or supplied stability cue. Do not claim that every energetically conceivable mode occurs or derive branching ratios without decay data.
Misconception
Gamma emission creates a new isotope because the nucleus loses energy. Gamma emission changes nuclear energy state without changing proton or neutron count, so A and Z remain the same.
Earlier objectives in this map
Decay and bombardment equations
Objective 2GC-NUC-DEC-02

Decay constant and half-life

Relate radioactive amount, decay constant, and half-life with N = N₀e⁻ˡᵃᵐᵇᵈᵃᵗ and λ = ln 2/t₁⁄₂ while preserving compatible time units.

Must know
For one radionuclide with a constant decay probability, N/N₀ = e⁻ˡᵃᵐᵇᵈᵃᵗ and λ = ln 2/t₁⁄₂; λ has inverse-time units and is not the same numerical quantity as half-life. N may represent nuclei, moles, mass, or activity-proportional amount when initial and final quantities use the same basis and no production or removal process is introduced.
Model boundary
Apply the supplied single-nuclide exponential model. Chemical Kinetics owns general experimental rate-law selection; Nuclear Reactions applies the first-order mathematics to radioactive decay without inferring a chemical mechanism.
Misconception
The decay constant and half-life are interchangeable because both describe how fast a sample decays. They are inversely related through λ = ln 2/t₁⁄₂ and carry reciprocal time dimensions.
Earlier objectives in this map
Parent–daughter changes by decay mode
Objective 3GC-NUC-DEC-03

Remaining fraction, age, and activity

Determine remaining fraction, elapsed time, sample age, or activity change from half-life or decay-constant data using repeated halves or logarithms as appropriate.

Must know
After n half-lives, the remaining fraction is (1/2)ⁿ; for a noninteger interval, the exponential or logarithmic form preserves the continuous decay model. Activity is decay rate and satisfies activity = λN for one nuclide, so activity and nuclide amount fall by the same fraction when λ is constant; becquerel and curie are activity units, not dose units.
Model boundary
Assume a closed sample, a constant half-life, and the named parent or measured activity unless production, daughter contribution, background, or an initial-condition correction is supplied. Do not infer absorbed dose from activity alone.
Misconception
A radioactive sample loses the same number of nuclei during every half-life interval. It loses the same fraction; the absolute number lost decreases as the remaining parent population decreases.
Earlier objectives in this map
Decay constant and half-life
DParticles3 objectives
Objective 1GC-NUC-PAR-01

Nuclear-particle notation and identity

Identify alpha particles, beta-minus particles, positrons, gamma photons, neutrons, and protons from their names, symbols, mass-number contribution, atomic-number contribution, and electric charge.

Must know
The nuclear-equation ledger pairs are α (A = 4, Z = 2), β⁻ (0, −1), β⁺ (0, +1), γ (0, 0), neutron (1, 0), and proton (1, 1). A beta-minus particle is an electron produced in a nuclear transformation, a positron is its positively charged antiparticle, and a gamma ray is a photon rather than a massive nucleon.
Model boundary
Use introductory particle identities and the notation supplied. Do not infer particle kinetic energy, spectrum, neutrino behavior, or detailed interaction cross sections from A, Z, and charge alone.
Misconception
A beta-minus particle is an ordinary orbital electron that was already stored inside the nucleus. It is produced during the nuclear transformation; its equation notation matches an electron’s charge and negligible nucleon count.
Earlier objectives in this map
Nuclide notation and particle inventory
Objective 2GC-NUC-PAR-02

Ionization, penetration, and shielding

Compare the introductory ionizing ability, penetration, external-versus-internal hazard, and shielding needs of alpha, beta, gamma, or supplied neutron radiation.

Must know
Alpha radiation is generally strongly ionizing but weakly penetrating, beta radiation is intermediate, and gamma radiation is deeply penetrating; shielding choice depends on radiation type, energy, and material. Low external penetration does not imply low internal hazard: source location, intake, distance, time, and attenuation affect exposure and dose.
Model boundary
Make qualitative comparisons under the stated conditions. Neutron shielding and all exact attenuation, range, dose, or biological-risk calculations require supplied material, energy, geometry, or conversion data.
Misconception
The least penetrating radiation is always the least hazardous. Hazard depends on source location and exposure conditions; alpha radiation can be especially damaging when an emitter is inhaled or ingested.
Earlier objectives in this map
Nuclear-particle notation and identity
Objective 3GC-NUC-PAR-03

Particle inference from nuclear change

Infer whether a particle was emitted or captured from the parent–daughter A/Z change and distinguish beta-minus, positron, electron-capture, gamma, neutron, and proton participation.

Must know
Compare parent and daughter A and Z first, then place the particle on the side required to close both ledgers; emission and capture of the same particle have opposite equation placement. Positron emission and electron capture produce the same daughter A/Z change but differ in reactants and emitted products, while gamma de-excitation leaves nuclide identity unchanged.
Model boundary
Use the stated participants or observed parent–daughter change. A/Z conservation may leave more than one physical pathway possible, so do not claim a unique mechanism when the equation evidence does not distinguish it.
Misconception
A one-step decrease in atomic number uniquely proves positron emission. Both positron emission and electron capture can produce that daughter change; the equation’s particle side or additional evidence distinguishes them.
Earlier objectives in this map
Nuclear-particle notation and identity · Parent–daughter changes by decay mode
ETerminology3 objectives
Objective 1GC-NUC-TER-01

Nuclide and decay vocabulary

Use nuclide, isotope, nucleon, radioisotope, radionuclide, parent, daughter, and decay-series terminology to describe a stated nuclear system precisely.

Must know
A nuclide is specified by its proton and neutron inventory; isotopes have the same Z but different A, and a nucleon is a proton or neutron. A radioisotope or radionuclide is unstable under the stated nuclear context, the parent is the nuclide before decay, and the daughter is the product nuclide after that step.
Model boundary
Use the terms for the evidence supplied. Isotope identity does not by itself specify abundance, stability, half-life, decay path, chemical state, or biological behavior.
Misconception
Nuclide and element are interchangeable because both are identified by a chemical symbol. An element is fixed by Z, while a nuclide also fixes neutron count or mass number; one element may have multiple nuclides.
Earlier objectives in this map
Nuclide notation and particle inventory
Objective 2GC-NUC-TER-02

Fission, fusion, and transmutation

Classify a supplied nuclear process as fission, fusion, transmutation, or a neutron-supported chain reaction and relate its energy direction to mass difference or binding-energy evidence.

Must know
Fission splits a heavy nucleus, fusion combines light nuclei, transmutation changes one element into another, and a chain reaction uses products such as neutrons to initiate additional events. Energy release is supported when products have lower total mass or greater binding energy under a consistent system boundary; the balanced equation still conserves A and Z.
Model boundary
Classify and compare supplied reactions. Reactor design, critical-mass geometry, stellar reaction networks, cross sections, reaction rates, and quantitative yields require explicit data and are not inferred from the process label alone.
Misconception
Fission and fusion are opposite names for any reaction that releases nuclear energy. Fission divides a heavy nucleus and fusion joins light nuclei; both may release energy under favorable binding-energy changes but are distinct processes.
Earlier objectives in this map
Mass-number and atomic-number conservation · Binding energy per nucleon and stability
Objective 3GC-NUC-TER-03

Activity, exposure, dose, and isotope use

Distinguish source activity, exposure conditions, absorbed dose, effective biological dose, tracer use, and therapeutic use from the quantities and context supplied.

Must know
Activity is decay rate, measured in becquerels (1 Bq = 1 decay/s) or curies (1 Ci = 3.7 × 10¹⁰ decays/s); absorbed dose is energy deposited per mass in gray (1 Gy = 1 J/kg), while sievert expresses a biologically weighted dose quantity. Activity alone does not determine exposure or dose: radiation type and energy, distance, time, shielding, geometry, uptake, distribution, and biological weighting may all matter.
Model boundary
Use supplied conversion factors, weighting factors, geometry, uptake, and biological data. Do not convert activity directly to Gy or Sv, equate medical tracer use with therapy, or infer individual risk from source activity alone.
Misconception
A source with twice the activity always gives a person twice the effective dose. Activity counts source decays; dose also depends on how radiation reaches and deposits energy in tissue and on the applicable weighting and exposure conditions.
Earlier objectives in this map
Remaining fraction, age, and activity · Ionization, penetration, and shielding

Free source ladder

Trace every nuclear claim.

Official 2026 DAT scopeDefines the five published topic labels—not their weights. ↗OpenStax · Nuclear Structure and StabilityNuclides, neutron–proton stability, mass defect, total binding energy, and binding energy per nucleon. ↗OpenStax · Nuclear EquationsParticle notation and the independent mass-number and atomic-number conservation ledgers. ↗OpenStax · Radioactive DecayParent–daughter changes, alpha and beta processes, electron capture, gamma emission, activity, and half-life. ↗OpenStax · Transmutation and Nuclear EnergyBombardment, fission, fusion, chain reactions, and the mass–energy basis of nuclear energy. ↗OpenStax · Uses of RadioisotopesTracer, diagnostic, and therapeutic contexts with isotope-property and half-life constraints. ↗OpenStax · Biological Effects of RadiationIonization, penetration, shielding, activity, absorbed dose, and biologically weighted dose quantities. ↗