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A 1,6-Conjugate addition attacks the delta carbon of an extended conjugated electrophile. The resulting extended enolate can be protonated at different sites; proton transfer or equilibration can favor a product retaining carbonyl–alkene conjugation.

Proton coupling across H-C-C≡C-H can resolve a small four-bond splitting. In a propargyl acetal this connects the acetal methine and terminal alkyne proton.

Acetic acid is a weak acid that partly transfers protons to water, supplying hydronium and negative ions. It is therefore a weak electrolyte in water.

Acid-base chemistry studies how chemical acids and chemical bases exchange protons or electron pairs. Here the focus is transfer of protons in water: a chemical acid donates a proton, and a chemical base accepts it. The resulting chemical equilibrium determines pH, while a buffer solution can resist changes in pH. This connects microscopic chemical reactions with a compact, measurable description of a chemical solution.

The important distinction is between how much chemical acid is present and how readily it transfers a proton. A weak acid and a strong acid at the same total concentration need not have the same pH. Conversely, two buffer solutions can have the same pH while containing very different total quantities of their chemical acids and chemical bases.

An acid-base titration adds measured quantities of a standardized chemical acid or chemical base to determine an initially unknown acid or base inventory through neutralization. Monitoring pH also constrains chemical equilibrium parameters such as the acid dissociation constant.

The added reagent is the titrant; a pipette selects an aliquot of the sample and a burette measures the added volume. Known stoichiometry converts this volume into amount of substance. This separates two questions that a single pH reading cannot answer: how much chemical acid is present, and how readily it donates a proton. A large inventory of weak acid can consume more titrant than a small inventory of strong acid despite having a higher initial pH.

A chemical acid can donate a proton, or accept an electron pair to form a covalent bond. The pH and buffer solution examples below use the former meaning. See IUPAC Gold Book, acid.

The acid dissociation constant quantifies the chemical equilibrium for loss of one proton from a chemical acid. In water, write the actual proton transfer as $\mathrm{HA}+{\mathrm{H}}_2\mathrm{O}\rightleftharpoons {\mathrm{H}}_3{\mathrm{O}}^{+}+{\mathrm{A}}^{-}$. Its full dimensionless equilibrium constant isThe usual aqueous acid dissociation constant uses the solvent convention with water thermodynamic activity approximated by one:Here hydrated hydrogen ions are understood; ${\mathrm{H}}^{+}$ is shorthand, not an isolated bare proton in the chemical solution. All thermodynamic activities and $K_a$ are dimensionless quantities, using consistent standard states. If water thermodynamic activity differs appreciably from one, retain it in the full equilibrium constant instead of silently mixing conventions.

With activity coefficients ${\gamma }_i$ and reference concentration $c^{\circ }=1\mathrm{mol}{\mathrm{L}}^{-1}$, put $a_i={\gamma }_i[i]/c^{\circ }$ for each solute. ThenThe last expression is the dilute ideal concentration approximation, not the definition in a nonideal chemical solution. Omitting $c^{\circ }$ instead produces a quotient with units of concentration; its numerical value depends on the chosen units. Do not take a logarithm of that dimensional quotient. Conditional concentration quotients can change with ionic strength even at fixed temperature, whereas the thermodynamic acid dissociation constant retains the activity coefficient corrections. The acid dissociation constant entry distinguishes these conventions.

At the same temperature, solvent and standard states, a larger acid dissociation constant, equivalently a smaller pKa, indicates a stronger tendency to donate a proton. It does not specify an analytical concentration, a pH, or a reaction rate. Composition and the weak acid mass and charge balances are needed to predict pH; chemical kinetics addresses how quickly the chemical equilibrium is approached.

An increase in oxidation state records oxidation; a decrease records reduction. Thus ${\mathrm{Fe}}^{2+}\to {\mathrm{Fe}}^{3+}$ raises the iron oxidation state by one, while ${\mathrm{MnO}}_4^{-}\to {\mathrm{Mn}}^{2+}$ lowers the manganese oxidation state from $+7$ to $+2$. Five iron ions supply the five-electron inventory required per permanganate ion.

In an acidic chemical solution, the complete half-reactions areFirst balance oxygen with four water molecules, then hydrogen with eight protons, and finally electric charge with five electrons. Multiply the iron half-reaction by five and add; the exchanged electrons cancel:Both sides contain one manganese, four oxygen, eight hydrogen and five iron chemical atoms, with net electric charge $+17e$. The ${\mathrm{H}}^{+}$ notation represents the acidic aqueous proton inventory; it does not imply bare protons moving independently of water. These half-reactions and their sum are the acidic balance used in the documented permanganate-iron titration.^[ref]

The coefficients predict amounts consumed, not a collision of five ions or an elementary reaction. Bulk chemical solution also contains compensating counterions, which are omitted from this net chemical equation. The hydrogen and oxygen oxidation states are unchanged; balancing their inventories remains essential even though they do not account for the exchanged electrons.

An active site is the region of an enzyme where a substrate binds and undergoes a chemical reaction. In a protein enzyme, it includes the amino acid residues that contact the substrate and those that directly assist catalysis. These roles can overlap: an amino acid side chain can both orient a substrate and participate in chemistry. The active site occupies only part of the folded protein; the remaining amino acid residues help establish its protein structure, stability and movement. An active site need not be a consecutive stretch of protein primary structure: protein folding can bring distant amino acid residues together. A ribozyme instead supplies an RNA active site. See Alberts et al., Molecular Biology of the Cell, Protein Function: binding sites and catalytic sites.

Binding and catalysis answer different questions. A protein binding site recognizes shape and chemistry through such interactions as hydrogen bonds, electrostatics and the hydrophobic effect. At an active site, appropriate positioning also helps a substrate reach the transition state of a chemical reaction. Some amino acid side chains transfer a proton; others participate transiently in a covalent bond. The enzyme-substrate complex is the associated enzyme and substrate, before conversion to a reaction product. Merely accumulating this complex does not establish rapid catalysis: stabilizing the bound substrate without sufficiently stabilizing the transition state can leave a large barrier. The important complementarity is chemical as well as geometric. See Geoffrey M. Cooper, The Cell, The Central Role of Enzymes as Biological Catalysts: substrate binding and transition-state stabilization.

The cartoon makes a useful experimental distinction. Changing a contacting amino acid residue might weaken substrate binding, change the reaction rate, or do both. Changing a distant amino acid residue can also disrupt the active site by changing protein folding. Therefore a loss of activity after a mutation alone does not locate a catalytic group: compare binding, protein structure and enzyme kinetics as well. This is an interpretation guide, not a report of a particular mutation experiment.

A concrete example is hexokinase: it transfers the terminal phosphate group of ATP to the $6$-position hydroxyl group of a sugar such as glucose. Specificity need not mean only one acceptable substrate: the hexokinase reaction class includes several possible acceptor sugars. Which are used, and at what reaction rates, depends on the particular enzyme and conditions. See Swiss Institute of Bioinformatics, ENZYME entry EC 2.7.1.1: hexokinase reaction and acceptor range.

Bennett and Steitz compared yeast hexokinase A crystallized with glucose against hexokinase B crystallized without glucose. X-rays scattered by the crystals supplied diffraction measurements from which the authors reconstructed protein structure; comparing coordinates located movement, rather than measuring a reaction rate. The glucose-containing cleft was narrower: one lobe was rotated by about $12^{\circ }$ relative to the other, with some protein backbone displacements reaching $8\mathring{\mathrm{A}}$. This makes the active site a moving arrangement of interacting groups, rather than a permanent hole. See William S. Bennett Jr. and Thomas A. Steitz, Glucose-induced conformational change in yeast hexokinase, PNAS 75 (1978), 4848–4852.

The structural comparison has two explicit limitations: different forms of hexokinase and different crystal environments were compared, and static coordinates do not record the order of binding and movement. Closure is consistent with induced fit, but those structures alone cannot exclude conformational selection. The solution experiment under induced fit addresses whether compaction also occurs outside a crystal.

ATP is a nucleotide consisting of adenosine, itself adenine joined to ribose, carrying three phosphate groups. From the ribose outward, these groups are labelled $\alpha$, $\beta$, and $\gamma$. ATP connects energy-supplying processes to energy coupling for synthesis and active transport; the same carrier can be regenerated and reused. ^[ref].

The net hydrolysis commonly used in energy coupling isHere ${\mathrm{P}}_i$ denotes inorganic phosphate. At buffered pH $7$, this biochemical shorthand groups the appropriate protonation states into pools and leaves proton exchange with the buffer solution implicit. An explicit, charge-balanced choice is ${\mathrm{ATP}}^{4-}+{\mathrm{H}}_2\mathrm{O}⟶{\mathrm{ADP}}^{3-}+{\mathrm{HP}{\mathrm{O}}_4}^{2-}+{\mathrm{H}}^{+}$, without implying these are the only chemical species present. See the IUBMB recommendations for biochemical thermodynamics.

The quoted textbook biochemical standard state value is approximatelyThis convention uses fixed pH $7$, temperature $298.15\mathrm{K}$ ($25{}^{\circ }\mathrm{C}$), reference pressure $100\mathrm{kPa}$ ($1\mathrm{bar}$), unit reference thermodynamic activities for dissolved reactants and reaction products, and water thermodynamic activity approximated by one. The prime indicates the fixed-pH biochemical convention. See OpenStax Biology 2e, 6.4: standard ATP hydrolysis value and Biology 2e, 6.2: biochemical standard conditions. This is a reference value, rather than a universal value inside a biological cell; precise tables must also specify chemical solution conditions and any magnesium ion binding convention. Different reference conventions and data treatments give different tabulated values, as discussed in Li et al., 2010: a database of thermodynamic quantities for biochemical reactions.

An exergonic reaction has a negative change in Gibbs free energy, so the overall ATP hydrolysis is favourable under those reference conditions. Breaking a chemical bond by itself costs energy; forming new chemical bonds can release energy. The net change compares all reactants with all reaction products, including their interactions with water and the entropy contribution. Calling the phosphate connection a "high-energy bond" describes a large favourable change in Gibbs free energy on hydrolysis, rather than energy released by bond breaking alone. See 7.5 Strengths of Ionic and Covalent Bonds and Cooper, The Cell: ATP and metabolic energy.

Composition changes the driving force. At the same fixed pH, temperature, pressure, and binding convention, write the molar reaction change asHere $R$ is the molar gas constant, $T$ the absolute temperature, and $a$ a dimensionless thermodynamic activity for a biochemical pool. Constant water thermodynamic activity is absorbed into the reference term; fixed pH accounts for buffered protons. The shorthand $\Delta G$ means transformed molar reaction Gibbs free energy change, ${\Delta }_r{G}^{\prime }$, rather than a finite sample's total change. The natural logarithm acts on a dimensionless reaction quotient, never on concentrations with units. See the IUBMB biochemical thermodynamics recommendations and the general equilibrium constant relation.

For a stipulated ideal dilute chemical solution, let $a_i=[i]/c^{\circ }$, with $c^{\circ }=1\mathrm{mol}{\mathrm{L}}^{-1}$. Choose $[\mathrm{ATP}]=5\mathrm{mmol}{\mathrm{L}}^{-1}$, $[\mathrm{ADP}]=0.5\mathrm{mmol}{\mathrm{L}}^{-1}$, and $[{\mathrm{P}}_i]=1\mathrm{mmol}{\mathrm{L}}^{-1}$, ignoring activity coefficient corrections and magnesium binding. These are illustrative inputs, not a claim about a particular biological cell. ThenandIncreasing $Q$ tenfold raises $\Delta G$ by $RT\ln 10\approx 5.708\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ at this temperature. Thus the ATP to ADP ratio and available inorganic phosphate matter, even with the same standard state value. These are local molar predictions at the stipulated composition, rather than a constant total yield as an isolated sample reacts.

Radioactive decay by emission of an alpha particle, leaving a daughter atomic nucleus with two fewer protons and two fewer neutrons.

The helium-four atomic nucleus, containing two protons and two neutrons. Its ground-state spin and isospin are zero. A quantized cubic four-Skyrmion supplies a corresponding nuclear state in the soliton description.

The Brookhaven proton synchrotron used for the Lederman-Schwartz-Steinberger two-neutrino beam experiment.

Luis Walter Alvarez's program extended the Glaser bubble-chamber experiment into large hydrogen bubble chambers and systematic analysis. His lecture credits John G. Wood, an accelerator technician, with early hydrogen tracks, and emphasizes technicians' responsibility for chamber development.^[ref]

Alvarez's 1956 report describes a ten-inch hydrogen bubble chamber in a steady magnetic field, exposed to a $700\mathrm{MeV}$ negative-pion beam for proton scattering. Liquid hydrogen was the target. Horizontal windows admitted illumination and stereo viewing; a shielded light source let bubble-scattered light reach the lenses. A temperature gradient initially restricted sensitivity near the top. Tilting and fast recompression improved uniformity.^[ref]

The same report compares tracks without a magnetic field against straightness expectations, testing spurious curvature. Multiple Coulomb scattering remained a limitation. This separates an instrumental check from the physical momentum inferred with the field on.^[ref]

The scientific opportunity is to turn a visible geometry into a test of an invisible intermediate state. The bubble-chamber pressure cycle prepares the sensitive target; bubble-chamber track readout supplies geometric measurements. Neither step alone identifies a particle resonance.

The Anderson positron track experiment identified a light positively charged particle, now called the Positron, by combining magnetic bending, loss of kinetic energy in lead, and particle range. Each observation answered a different question: bending constrained momentum, the lead supplied a direction of travel, and particle range tested the proposed mass.

Carl David Anderson's The Positive Electron (1933), pp. 491–493, describes the 1932 discovery in a vertical cloud chamber with a $15,000\mathrm{gauss}$ magnetic field. A $6\mathrm{mm}$ lead plate separated two photographed track segments. The effective viewing depth was $1\mathrm{cm}$ along the magnetic field, with $14\mathrm{cm}$ transverse diameter: this restricted out-of-plane motion. The photographic readout supplied curvature on both sides. Comparisons with electron tracks under the same conditions constrained ionization; specific ionization was not directly measured for these events. He tested accidental alignment of unrelated tracks and rejected a reversed electron interpretation requiring an increase of kinetic energy in lead. Assuming unit electric charge, the mass bound was about twenty electron masses, rather than an exact mass determination. The paper credits Robert Andrews Millikan with the design and Seth Henry Neddermeyer with assistance.^[ref]

Preparation used rapid piston expansion and a water–alcohol mixture in the cloud chamber; cooling permitted droplets to form along ionization trails. A camera photographed these droplets. Initially, expansions occurred at random, so many photographs contained no tracks. Later counter triggering improved the useful yield.^[ref]

In The Production and Properties of Positrons, his 1936 lecture, Carl David Anderson describes the chamber inside an electromagnet and explains why the lead plate was decisive: after losing kinetic energy, a particle bent more sharply. He describes a proton hypothesis predicting only $5\mathrm{mm}$ of particle range, against an observed path longer than $50\mathrm{mm}$. These are historical values from the lecture, not the stipulated example below. The point was the incompatibility of particle range with the momentum inferred from curvature, rather than positive electric charge alone.^[ref]

Occupying an antibonding molecular orbital opposes a chemical bond. For equivalent $1s$ atomic orbitals of the hydrogen atom, the difference ${\sigma }_u^{\ast }={\sigma }_{-}$ vanishes on the plane halfway between the protons: every point there is equally far from both centres, so the amplitudes cancel. This nodal plane removes the contribution of this molecular orbital to electron density on that plane; it does not make an entire finite region empty. The $1s$-derived antibonding molecular orbital lies above its bonding molecular orbital partner in energy. See Field, MIT 5.61, lecture 25, pp. 1–2.

In the ${\mathrm{He}}_2$ minimal model, $({\sigma }_u^{\ast }{)}^2$ adds $N_a=2$ and cancels the bond order contribution of $({\sigma }_g{)}^2$. Opposite signs on the two lobes describe probability amplitudes, while both lobes have nonnegative probability density after squaring. The star is an orbital label, not an extra electron or an electric charge.

Antiperiplanar geometry places two specified bonds at a torsion near $180^{\circ }$. It often enables favorable orbital alignment in E2 elimination and supports large vicinal proton couplings in an appropriate calibrated Karplus relation.

The antiproton is the antiparticle of the proton: it has the same rest mass and spin $1/2$, with opposite electric charge and baryon number. A negative electric charge alone cannot identify an antiproton, because a negative pion also bends in that direction in a magnetic field. Combining magnetic rigidity with velocity determines a rest mass; agreement with the proton rest mass then makes the identification much more discriminating.

The mode expansion of a Dirac field explains how independent particle and antiparticle excitations enter a relativistic field description. It supplies a theoretical language for the antiproton, while the Chamberlain-Segrè antiproton identification supplies an experimental test. The proton is a composite baryon, so a free Dirac field is not a complete account of its internal dynamics or of antiproton production in a target.

Argon-40 is a stable isotope with 18 protons and 22 neutrons. Radiogenic argon-40 accumulated from potassium-40 is a daughter product used in potassium-argon dating.

The central system of protons and neutrons in an atom. Its mass number $A$ is its baryon number in ordinary nuclear states; $Z$ is the proton number and $N$ the neutron number.

The nucleus contains almost all of an atom's mass and carries positive electric charge $Ze$, where $e$ is the elementary charge. The atomic number $Z$ identifies the chemical element; changing $N$ at fixed $Z$ gives another isotope. The mass number $A=Z+N$ counts nucleons, rather than specifying the exact nuclear mass: nuclear binding energy lowers the mass of a bound system relative to its separated constituents. The simplest nucleus is a single proton; other atomic nuclei can contain many protons and neutrons bound by the nuclear force.

A nuclear quantum state has properties such as spin and a spatial nuclear charge distribution. These are different questions from merely counting nucleons. A small-angle elastic scattering measurement can reveal a nuclear charge radius, while a wider range of momentum transfer tests the distribution's shape. The Hofstadter nuclear electron scattering experiment made this connection between scattering patterns and nuclear structure experimentally concrete.