AP Physics 2

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Topic chapters: Thermal physics and gases

• 9.1 Kinetic Theory of Temperature and Pressure

  Common misconceptions

  • “At thermal equilibrium all atoms move at the same speed.” A distribution of speeds remains. Equal temperature means equal average translational kinetic energy, not identical atom speeds.
  • “A heavier gas must be hotter if it has more total kinetic energy.” Temperature tracks average energy per atom. Total energy also depends on how many atoms there are.
  • “Pressure only exists where gas hits a real wall.” A small imagined surface anywhere in a gas experiences momentum exchange from atoms on both sides; pressure is a local property.

  Teaching notes

  • Work through the two-atom component-table example before assigning q01. Ask students to write two separate momentum equations and then perform the total kinetic-energy check; momentum conservation alone does not establish an elastic collision.
  • Ask students to draw incoming and outgoing velocity components before calculating an impulse. The normal component reverses at an ideal smooth wall; the tangential component does not.
  • For two gases at the same temperature ask separately about average kinetic energy, rms speed, and total internal energy. These are different questions.
  • Use qualitative distribution sketches. Do not require the functional formula of the Maxwell–Boltzmann distribution or three-dimensional collision calculations.

• 9.2 The Ideal Gas Law

  Common misconceptions

  • “If the temperature doubles in degrees Celsius, pressure doubles.” Gas-law ratios require kelvin. For example, 20 °C to 40 °C changes 293 K to 313 K, a much smaller ratio.
  • “PV is always constant.” PV is constant only when both amount and temperature are fixed.
  • “Extrapolating a gas graph proves a real gas remains gaseous to absolute zero.” Extrapolation describes the ideal model; real gases often liquefy before that limiting state.

  Teaching notes

  • Have students annotate fixed N, V, P, or T directly on each graph.
  • Check use of absolute pressure if a device reports gauge pressure. Add ambient pressure before applying PV = nRT.
  • Accept a zero-pressure intercept close to −273 °C from uncertain data, with an explanation of the ideal-model extrapolation.

• 9.3 Thermal Energy Transfer and Equilibrium

  Common misconceptions

  • “An object contains heat.” An object has internal energy. Heat describes transfer across a boundary because of a temperature difference.
  • “Equal temperatures mean no atom-level energy exchanges occur.” Collisions and radiation can still exchange energy in both directions; equilibrium means no net thermal transfer.
  • “The larger or more energetic object always heats the smaller one.” The spontaneous net direction depends on temperature, not total energy or mass.

  Teaching notes

  • Use arrows crossing a drawn boundary. Ask whose Q is positive and whose is negative for the same interaction.
  • Ask students to classify mechanism and direction separately: radiation can carry energy across empty space; direction follows temperature.
  • At equilibrium press for the words no net transfer, rather than no transfer.

• 9.4 The First Law of Thermodynamics

  Common misconceptions

  • “An isothermal expansion has Q = 0.” For an ideal gas ΔU = 0 when T is fixed, but expansion gives W_on < 0. Heating supplies Q = −W_on > 0.
  • “Work is a property stored in a state.” Work is a transfer that depends on the path. Internal energy is a state property.
  • “Compression always cools a gas.” Adiabatic compression adds energy by work and heats it. Cooling can occur if enough energy leaves thermally.
  • “A closed system cannot exchange energy.” Closed means matter does not cross its boundary. Energy can cross by heat or work; an isolated system exchanges neither matter nor energy.

  Teaching notes

  • Require a signed energy ledger before substitution: Q into gas positive, W_on from compression positive.
  • On each PV path, mark direction. The area alone gives a magnitude; expansion or compression gives the work sign.
  • Keep U = 3nRT/2 explicitly limited to an ideal monatomic gas; it is not a formula for solids or arbitrary molecular gases.
  • When using gas pressure for PV work, state slow mechanical equilibrium with the external pressure. For irreversible expansion use external pressure, not an unspecified gas pressure.

• 9.5 Specific Heat and Thermal Conductivity

  Common misconceptions

  • “Specific heat and heat capacity are the same quantity.” Specific heat c is energy per kilogram per kelvin; the sample’s heat capacity mc also depends on its mass.
  • “A material with high conductivity must have low specific heat.” Conductivity and specific heat describe different microscopic behavior. One governs transfer rate; the other energy required for a temperature change.
  • “A thick insulator changes its material conductivity.” Its geometry changes transfer rate, but the material’s intrinsic k stays the same under the stated conditions.

  Teaching notes

  • For calorimetry, students should name the combined system and every omitted energy store before setting energy gained equal to energy lost.
  • Use the AP approximation of temperature-independent c, and avoid unprovided phase changes in Q = mcΔT problems.
  • A steady conduction experiment needs two maintained boundary temperatures. A warming sample’s transient temperature curve is not automatically a measurement of k.

• 9.6 Entropy and the Second Law of Thermodynamics

  Common misconceptions

  • “Entropy is simply the everyday messiness of an object.” Use the distribution of energy and the system’s thermodynamic state. Visual untidiness by itself is not a reliable thermodynamic measure.
  • “If entropy rises, some energy disappears.” Energy remains conserved. It becomes more dispersed and less available to produce organized work under the given conditions.
  • “Entropy of every object must increase.” A closed object can lose entropy through its surroundings. The entropy of the isolated combined system cannot decrease.
  • “Two paths to the same final state produce different changes in the object’s entropy.” The object’s entropy is a state function, so the same endpoints give the same change; total entropy generation can differ.

  Teaching notes

  • Ask students to draw a larger boundary including the surroundings when a subsystem’s entropy decreases.
  • Qualitative arguments are the AP requirement. Do not require ΔS = Q_rev/T, logarithmic gas formulas, or statistical entropy calculations.
  • Distinguish entropy change of a returning cyclic device from entropy change of the device plus reservoirs.
  • Describe reversible as an ideal limit that can be undone leaving no net change in both system and surroundings; ordinary finite-temperature-difference heat transfer is irreversible.

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Topic chapters: Charge and electric fields, Electric energy, potential, and capacitors

• 10.1 Electric Charge and Electric Force

  Common misconceptions

  • “A larger charge feels the larger force in a two-object interaction.” Both forces have magnitude k|q₁q₂|/r²; differing accelerations can come from different masses.
  • “Neutral material has no electric forces.” Neutral matter contains charged constituents; microscopic electric interactions also underlie contact forces.

  Teaching notes

  • Ask students to explain force direction without using a negative magnitude.
  • Have students state the point-charge and medium assumptions before using Coulomb’s law.
  • Diagnose scale reasoning with a neutral planet versus a charged dust grain.

• 10.2 Conservation of Electric Charge and the Process of Charging

  Common misconceptions

  • “Rubbing creates negative charge.” Electrons transfer between objects; the combined system’s charge is conserved.
  • “Any grounded object must become neutral immediately.” A nearby charged source can maintain an induced net charge while the object is at ground potential.

  Teaching notes

  • Have students draw a boundary for object-only and object-plus-Earth systems.
  • Ask which step crosses that boundary and which merely changes distribution.
  • Use identical spheres only when claiming equal final charge.

• 10.3 Electric Fields

  Common misconceptions

  • “Electric field points in the direction an electron accelerates.” Field direction uses positive charge; an electron’s acceleration is opposite.
  • “Field lines are charged-particle trajectories.” They show force direction at each place. A particle’s existing velocity can make its path differ.

  Teaching notes

  • Require separate source-field sketches before net vectors.
  • Ask why a tangential surface field contradicts conductor equilibrium.
  • Use qualitative reasoning only for fields within general insulators.

• 10.4 Electric Potential Energy

  Common misconceptions

  • “Negative energy means negative force magnitude.” Energy is a signed scalar relative to a reference. A force magnitude is nonnegative, with direction treated separately.

  Teaching notes

  • Ask students to narrate the sign of external work before multiplying numbers.
  • Have them list pair labels to expose double counting.

• 10.5 Electric Potential

  Common misconceptions

  • “Potential is a vector because electric field is a vector.” Potential is signed energy per charge; add it as a scalar.
  • “A charged conductor must have zero potential because its internal field is zero.” Zero internal field implies one constant potential; its value depends on the reference and configuration.

  Teaching notes

  • Have students make both scalar and vector predictions at a dipole midpoint.
  • Ask for contour labels and normal distance before estimating E.

• 10.6 Capacitors

  Common misconceptions

  • “A capacitor stores a net charge Q.” The ideal plates carry +Q and −Q; Q labels a plate-charge magnitude and the complete capacitor has zero net charge.
  • “Adding a dielectric always decreases capacitor energy.” It decreases energy at fixed charge but increases it at fixed voltage; the battery participates in the latter energy transfer.

  Teaching notes

  • Require a constraint statement before factor-of-change predictions.
  • Ask students to connect the triangular area of the V versus Q graph to work.
  • Check that projectile calculations satisfy the stated gap and negligible-edge assumptions.
  • Distinguish the area under capacitor voltage versus charge (stored energy/minimum quasistatic assembly work) from constant-voltage battery energy QV. In ordinary RC charging the remainder is resistor heating.

• 10.7 Conservation of Electric Energy

  Common misconceptions

  • “Every charged particle speeds up toward lower potential.” Positive charges do; negative charges can gain kinetic energy toward higher potential.
  • “Potential difference by itself sets speed.” Charge, mass, initial kinetic energy, and any other work also matter.

  Teaching notes

  • Ask students to draw energy bars and state whether external work is included.
  • Use a turning-point question to expose negative-K arithmetic as a physical impossibility.
  • Ask whether all velocity components vanish at the proposed turning point. Without one-dimensional motion, K₀/q gives an energy accessibility bound rather than a guaranteed turning-potential rise.

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Topic chapters: Current, resistance, and circuits

• 11.1 Electric Current

  Common misconceptions

  • “The battery sends newly created electrons through a bulb.” Mobile charges already occupy the conducting circuit; the source transfers energy and maintains a potential difference.
  • “No current means no electron motion.” It means no net organized charge flow, while random motion remains.

  Teaching notes

  • Have students distinguish a charge-flow rate from carrier drift speed.
  • Ask students to redraw electron arrows without changing the conventional-current schematic.

• 11.2 Simple Circuits

  Common misconceptions

  • “An open circuit has no voltage anywhere.” It lacks a conducting path through the break, but sources and the open gap can have nonzero potential difference.
  • “Any two components drawn side by side are parallel.” They must connect to the same two nodes.

  Teaching notes

  • Have students build one schematic then redraw it in two shapes.
  • Use the symbol figure and require students to identify a variable-element arrow.
  • Check the battery’s shared membership in both loops.

• 11.3 Resistance, Resistivity, and Ohm’s Law

  Common misconceptions

  • “Every ohmic metal has temperature-independent resistivity.” Constant-R ohmic behavior is usually specified at a controlled temperature. Real metallic ρ can rise with temperature; the temperature-independent idealization must be named.
  • “I-versus-V slope equals resistance.” It equals 1/R; a V-versus-I slope equals R.

  Teaching notes

  • Read both axes aloud before extracting R.
  • Have students identify which assumptions make constant ρ legitimate.
  • Use low-current readings and cooldowns in resistance measurements.

• 11.4 Electric Power

  Common misconceptions

  • “Current is used up as light is produced.” Energy is transferred and converted; charge flow is conserved through an unbranched bulb path.
  • “Battery voltage can be used in every resistor’s P = V²/R.” Only use the voltage across the element whose power you are finding.

  Teaching notes

  • Demand a fixed-current or fixed-voltage statement in brightness comparisons.
  • Ask students to check battery supplied power against sum of resistor powers.

• 11.5 Compound Direct Current (DC) Circuits

  Common misconceptions

  • “All parallel branches carry the same current.” They share voltage; branch current depends on each resistance.
  • “Battery emf always equals terminal voltage.” A discharging nonideal battery loses Ir internally; emf is its open-circuit voltage.
  • “A voltmeter belongs in the same series path as the resistor.” It connects across the resistor’s endpoints; an ideal series voltmeter would interrupt current.

  Teaching notes

  • Check endpoints before reduction.
  • Have students recover branch values after finding equivalent resistance.
  • Ask why neglecting wire resistance fails in a nearly shorted loop.

• 11.6 Kirchhoff’s Loop Rule

  Common misconceptions

  • “Every resistor is a negative term in every loop equation.” It is negative when traversal follows current and positive when traversal goes against current.
  • “Every drawable loop adds an independent equation.” Some loop equations follow from others; use independent loops to solve, additional loops to check.

  Teaching notes

  • Require students to point to a physical element for each algebraic term.
  • Ask them to redraw their potential graph after changing only the reference.
  • Use explicit branch currents rather than ambiguous I labels.

• 11.7 Kirchhoff’s Junction Rule

  Common misconceptions

  • “The current divides equally at every junction.” Branch currents depend on resistances and shared voltage; equality needs symmetry.
  • “A negative solved current means the circuit is impossible.” It generally means the actual direction opposes your assumed arrow.

  Teaching notes

  • Ask for a region boundary around the junction and charge amounts over one second.
  • Require a final arrow redraw when a solution is negative.

• 11.8 Resistor-Capacitor (RC) Circuits

  Common misconceptions

  • “An uncharged capacitor acts like a wire forever.” It has zero voltage only initially; its branch current decreases as voltage builds, approaching an open-circuit endpoint.
  • “Charge crosses the insulating gap while the capacitor charges.” Charge reaches one plate and leaves the other through external wires; the ideal dielectric does not conduct across the gap.
  • “Every capacitor in series has equal voltage.” The standard series string has equal charge magnitude; voltage is Q/C and can differ.

  Teaching notes

  • Require initial state before choosing a wire or open-circuit model.
  • Ask whether other branches still conduct at the final time.
  • Use qualitative transient curves and τ landmarks; avoid exponential/logarithmic assessment.

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Topic chapters: Magnetism and induction

• 12.1 Magnetic Fields

  Common misconceptions

  • “Magnetic field lines begin at north and end at south.” Only the outside part looks that way. Follow the line through the magnet: it is closed.
  • “Any iron sample must already be a strong permanent magnet.” Domains can cancel at the sample scale. Composition enables ferromagnetism; domain arrangement determines the net magnetization.
  • “Permeability is always one fixed material constant.” Use the value for the specified temperature, orientation, and field strength.

  Teaching notes

  • Have students draw a full loop, including the magnet interior, before using a compass.
  • Ask students to explain why a uniformly magnetized sample can still have two poles after cutting.
  • Separate compass torque from a net translational force.

• 12.2 Magnetism and Moving Charges

  Common misconceptions

  • “A negative charge has a negative force magnitude or radius.” Use |q| in magnitudes and radius. Its sign reverses the force direction.
  • “Magnetic force accelerates a particle by making it faster.” Acceleration can change direction only. A magnetic-only force does no work.
  • “The magnetic field created by a charge points along the force on that charge.” The source field and force are different vectors governed by different right-hand-rule inputs.

  Teaching notes

  • Require a labeled v, B, and F diagram before calculations.
  • Quantitative moving-charge force questions use 0°, 90°, and 180°; discuss other angles qualitatively.
  • The magnetic model is nonrelativistic and must keep v below c.

• 12.3 Magnetism and Current-Carrying Wires

  Common misconceptions

  • “The field of a straight wire points away from the wire.” It is tangent to a circle centered on the wire, with no radial component.
  • “Add the field magnitudes of two wires before checking directions.” Determine each local vector first; opposite fields subtract.
  • “Use the whole wire length in IℓB.” Only the portion inside the stated field belongs in ℓ.

  Teaching notes

  • Use a compass map and then replace compass needles with tangent arrows.
  • Ask for a straight-line B versus 1/r graph with slope units.
  • Require separate diagrams for a source’s own field and force from an external field.

• 12.4 Electromagnetic Induction and Faraday’s Law

  Common misconceptions

  • “Lenz’s law always makes a field opposite the existing field.” It opposes the change. A decreasing field is supported by a field in the same direction.
  • “The angle in BA cos θ is measured from the surface.” Measure from its perpendicular area vector.
  • “A generator gets electrical energy directly from a static magnetic field.” An external agent supplies work against the induced resisting force.

  Teaching notes

  • Have students choose one normal and associated positive circulation before assigning algebraic signs.
  • Distinguish an induced emf from a current; a closed path is needed for sustained current.
  • Use piecewise linear flux graphs so AP algebra gives the interval emfs.

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Topic chapters: Light rays and images

• 13.1 Reflection

  Common misconceptions

  • “A ray lies along a wavefront.” A ray is perpendicular to a wavefront and points in the propagation direction.
  • “Reflection angles are measured from the mirror surface.” The law uses the normal, perpendicular to the local surface.
  • “Diffuse reflection breaks the reflection law.” Every local patch obeys the law; its normal differs from neighboring patches.

  Teaching notes

  • Draw arrows on incident and reflected rays; missing arrows can hide a reversed path.
  • Use a mirror and matte paper to compare reflected directions at the same incident angle.
  • Discuss laser ray models alongside a slit demonstration, while leaving interference calculations to Unit 14.

• 13.2 Images Formed by Mirrors

  Common misconceptions

  • “A negative image distance is an impossible answer.” It identifies a virtual image behind the mirror in the chosen convention.
  • “A mirror focus is at its center of curvature.” For near-axis rays it is approximately halfway there.
  • “All virtual mirror images are reduced.” A concave mirror used inside its focal length gives an enlarged virtual image.

  Teaching notes

  • State the optical sign convention on the board and reuse it for every problem.
  • Ask learners to point to actual ray intersections before calling an image real.
  • Limit mirrors to plane, concave spherical, and convex spherical; use near-axis rays for spherical equations.

• 13.3 Refraction

  Common misconceptions

  • “Light changes frequency when it enters glass.” A stationary boundary keeps the source frequency fixed; speed and wavelength change.
  • “Any sufficiently steep incidence can cause total internal reflection.” The ray must first be going from higher index to lower index.
  • “An inverse-sine input above one means round the angle to 90°.” It means no real transmitted ray exists under the stated conditions.

  Teaching notes

  • Have learners identify medium 1 from the incoming arrow, rather than from table order.
  • Use a semicircular block so the incoming ray can enter normally at its curved surface; this isolates refraction at the flat face.
  • Check the two TIR conditions in words before calculating a critical angle.

• 13.4 Images Formed by Lenses

  Common misconceptions

  • “A convex lens always forms a real image.” A real object inside its focal length gives an upright enlarged virtual image.
  • “Both lens focal points are used the same way for every ray.” For a converging lens, parallel incident rays head through the far focus; near-focus incident rays exit parallel.
  • “The image is negative because it is left on the drawing.” Optical signs distinguish real and virtual; the drawing can be reversed without changing those signs.

  Teaching notes

  • Begin with a labeled object, lens midline, both foci, and travel direction.
  • Pair a screen projection outside f with direct viewing through the lens inside f.
  • The rays model supports thin-lens and Snell/TIR cases; use static sketches for mirrors and diverging-lens details.

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Topic chapters: Waves and sound, Light as a wave

• 14.1 Properties of Wave Pulses and Waves

  Common misconceptions

  • “The crest is a piece of matter traveling down the rope.” A crest is a moving pattern. Follow a mark on the rope to see local oscillation while the disturbance and energy travel.

  Teaching notes

  • Mark one rope segment and ask whether it reaches the far end. Ask students to identify compression from a pressure graph rather than from a drawing of particles.

• 14.2 Periodic Waves

  Common misconceptions

  • “The distance between two crests on any graph is wavelength.” Check the horizontal units: crest separation in seconds is period; separation in meters is wavelength.

  Teaching notes

  • Show identical-looking curves with x and t axes and ask which gives wavelength. Ask what is being held fixed before an energy comparison.

• 14.3 Boundary Behavior of Waves and Polarization

  Common misconceptions

  • “An inverted reflected wave has negative frequency.” Inversion is a π phase reversal of signed displacement; frequency remains the positive repetition rate.

  Teaching notes

  • Use two strings at the same tension to establish the speed/phase rule. Do not generalize that rule to arbitrary impedance systems without specifying the model.

• 14.4 Electromagnetic Waves

  Common misconceptions

  • “Light needs vibrating air because it is a wave.” The oscillating quantities are electric and magnetic fields; no material medium is required.

  Teaching notes

  • Require three mutually perpendicular arrows. Assess spectrum order, not memorized numerical category boundaries.

• 14.5 The Doppler Effect

  Common misconceptions

  • “A moving siren makes sound travel faster through the air.” Ordinary sound speed relative to the air is a medium property; the source changes the spacing of emitted fronts.

  Teaching notes

  • Use source emission dots separated by equal times; compare moving source with moving observer. Quantitative sound Doppler expressions are enrichment, not required assessment.

• 14.6 Wave Interference and Standing Waves

  Common misconceptions

  • “The second resonance of a closed–open pipe is its second harmonic.” Only odd harmonics fit those boundaries; the second resonance is the third harmonic.

  Teaching notes

  • Ask students to add displacements at several x values, not just peaks. Diagnose whether pipe diagrams show displacement or pressure.

• 14.7 Diffraction

  Common misconceptions

  • “The central dark minimum has m = 0.” At zero path difference the slit contributions reinforce; the center is bright. Dark minima start at nonzero m.

  Teaching notes

  • Have students pair the top and bottom halves of a slit at the first minimum. Distinguish single-slit minima from double-slit maxima.

• 14.8 Double-Slit Interference and Diffraction Gratings

  Common misconceptions

  • “Every bright fringe in a real double-slit pattern has equal intensity.” Its finite-width slits supply an envelope that modulates brightness and can remove orders entirely.

  Teaching notes

  • Ask for both a and d on every sketch. Require sin θ ≤ 1 before accepting a grating order.

• 14.9 Thin-Film Interference

  Common misconceptions

  • “A quarter vacuum wavelength is always the best film thickness.” Use the wavelength inside the coating and inspect both reflection phases. The quarter-wave rule here is λ₀/(4n) for an intermediate-index antireflection layer at normal incidence.

  Teaching notes

  • Make a two-row interface table first. Complete cancellation requires suitable amplitudes as well as opposite phase; a quarter-wave thickness alone can only minimize reflection.

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Topic chapters: Quantum, atomic, and nuclear models

• 15.1 Quantum Theory and Wave-Particle Duality

  Common misconceptions

  • “A massless photon cannot carry momentum.” Zero rest mass does not mean zero energy. A vacuum photon has momentum E/c.

  Teaching notes

  • Require the student to name the observation that needs the model. Use vacuum photon momentum only unless a different medium model is explicitly provided.

• 15.2 The Bohr Model of Atomic Structure

  Common misconceptions

  • “The number written above the element is the number of neutrons.” A is the total nucleon number. Subtract Z to find neutrons.

  Teaching notes

  • Ask students to keep separate counts of protons, neutrons, and electrons. Explain that circular Bohr orbits are a model, not a required modern picture of literal electron paths.

• 15.3 Emission and Absorption Spectra

  Common misconceptions

  • “A −3 eV energy level emits a 3 eV photon whenever an electron occupies it.” Emission needs a downward transition; its photon energy is the difference between two levels.

  Teaching notes

  • Ask which levels are occupied before listing absorption lines. Do not allow “any photon greater than a transition energy works” for a bound-to-bound transition.

• 15.4 Blackbody Radiation

  Common misconceptions

  • “A blackbody emits only at its peak wavelength.” It emits a continuous distribution; Wien’s law locates the greatest spectral contribution, not the only wavelength.

  Teaching notes

  • Require both peak-position and integrated-area comments on a spectral graph. Do not infer true temperature from an uncalibrated phone photograph’s color.

• 15.5 The Photoelectric Effect

  Common misconceptions

  • “Brighter monochromatic light produces greater stopping voltage.” At fixed frequency it supplies more photons, but maximum electron energy and ideal stopping voltage stay fixed.

  Teaching notes

  • Require a threshold check before computing Kmax. Ask why the current can change without changing stopping voltage.

• 15.6 Compton Scattering

  Common misconceptions

  • “A Compton photon keeps its momentum because photons always travel at c.” Speed c stays fixed in vacuum, but energy, wavelength, and momentum magnitude can change in the interaction.

  Teaching notes

  • Use the scattering angle between incoming and outgoing photon directions. Require both momentum components; do not use nonrelativistic electron kinetic energy when recoil is relativistic.

• 15.7 Fission, Fusion, and Nuclear Decay

  Common misconceptions

  • “Exactly half of any small collection must disappear each half-life.” Half-life predicts an expected population fraction. Finite counts fluctuate and individual decay times remain unpredictable.

  Teaching notes

  • Check all reactants and products, including emitted nucleons. Require a consistent nuclear-mass or atomic-mass convention; ask what the clock predicts for one nucleus versus a sample.

• 15.8 Types of Radioactive Decay

  Common misconceptions

  • “Beta-minus ejects an electron that was already orbiting the atom.” The electron is emitted when a neutron changes into a proton, with an antineutrino; nuclear Z increases.

  Teaching notes

  • Use electrons and neutrinos with positive lepton number, their antiparticles negative, only for conservation bookkeeping. Do not require neutrino flavors or isotope-pathway memorization.

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