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An enol stabilized by an intramolecular O–H···O interaction, commonly closing a six-membered arrangement in a 1,3-dicarbonyl compound. proton exchange between equivalent enol forms can average NMR environments.

A chemical element is an identity shared by all chemical atoms whose atomic nuclei contain the same number of protons. That number is its atomic number, $Z$: six means carbon, eleven means sodium. The identity survives differences in neutron count, which distinguish isotopes, and differences in electron count, which distinguish neutral chemical atoms from ions. See the IUPAC Gold Book, chemical element.

The same name can also denote a pure chemical substance containing only that chemical element. These two uses answer different questions. Molecular oxygen, ${\mathrm{O}}_2$, is a chemical substance made entirely of oxygen; water, ${\mathrm{H}}_2\mathrm{O}$, is a chemical compound containing both hydrogen and oxygen. A water molecule contains three chemical atoms but only two chemical elements. Joining chemical atoms through chemical bonds changes their arrangement without changing their atomic numbers.

This distinction makes stoichiometry possible: ordinary chemical reactions rearrange chemical atoms, so one can count each chemical element before and after a transformation. Changing the proton count instead changes the chemical element and requires a nuclear reaction. The periodic table organizes these identities into a useful map, while atomic number bookkeeping keeps identity, isotope, and electric charge separate.

Chemiosmosis couples transmembrane ion movement down an electrochemical gradient to a chemical transformation. For mitochondrial ATP synthesis, protons return from the intermembrane space to the mitochondrial matrix through ATP synthase.^[ref]

An original thermodynamic example separates the electrical and chemical contributions. At fixed temperature $T$, use ideal dilute thermodynamic activities $a$ and the electric potential $\psi$ on each side. The molar electrochemical potential difference for inward transfer of a singly charged proton isHere $R$ is the molar gas constant, $F$ the Faraday constant, and $\ln$ the natural logarithm. The sign convention is destination minus origin: a negative difference makes inward transfer favourable. Both lower proton activity and a more negative electric potential inside favour inward movement.

Stipulate $T=300\mathrm{K}$, $a_{\mathrm{matrix}}/a_{\mathrm{outside}}=0.1$, ${\psi }_{\mathrm{matrix}}-{\psi }_{\mathrm{outside}}=-0.12\mathrm{V}$, $R=8.314\mathrm{J}\mathrm{mo}{\mathrm{l}}^{-1}{\mathrm{K}}^{-1}$ and $F=96485\mathrm{C}\mathrm{mo}{\mathrm{l}}^{-1}$. These illustrative inputs give approximately $-5.743$ and $-11.578\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ for the chemical and electrical terms, hence $-17.321\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ per transferred proton. For a hypothetical device coupling three inward protons per ATP to an ATP-formation cost of $45\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$,The sign follows by adding changes in the state function Gibbs free energy. It establishes thermodynamic feasibility for this chosen model, not its reaction rate. Three is a stipulated coupling count, not a universal ATP synthase stoichiometry; transport costs and leaks can also consume the available free energy.

James H. Christenson, James Watson Cronin, Val Logsdon Fitch and René Turlay reported the result in 1964. At Brookhaven's AGS, 30 GeV protons struck beryllium; collimators selected a neutral particle beam at 30 degrees. A downstream helium decay volume reduced interactions.^[ref]

The flight distance suppressed the short-lived kaon component. Each arm of a two-arm magnetic spectrometer had spark chambers before and after its magnet. Cherenkov detectors and scintillation counters triggered photographic recording in coincidence.^[ref]

The helium sample yielded $45\pm 9$ signal events; $(2.0\pm 0.4)\times 10^{-3}$ was the ratio to all charged decay channels.^[ref] That denominator must be retained when comparing this result with a total branching fraction.

The evidence was kinematic. Later regenerated-beam quantum interference established that the short- and long-lived states reached the same two-pion final state, excluding alternatives such as distinct pion-like particles.^[ref] The 1964 observation established evidence for CP violation; it did not determine every parameter of the CKM matrix. Inferring time-reversal symmetry violation from CP violation invokes CPT symmetry, rather than a direct comparison of time-reversed transitions in that experiment.

vicinal coupling between protons on the same side of an alkene. A measured first-order splitting is an approximation if the spin system is appreciably strongly coupled.

In 1932 John Douglas Cockcroft and Ernest Thomas Sinton Walton accelerated hydrogen ions from a discharge source through an evacuated tube onto lithium at $45^{\circ }$. A side-facing zinc sulfide screen, viewed by microscope, showed particle scintillations. Mica stopped scattered protons; switching off or blocking the beam removed the flashes. An external screen allowed absorption-range measurements.^[ref]

Magnetic deflection checked voltage calibration. Opposite screens and independent observers found excess coincidences for a thin lithium target, supporting paired alpha particle emission; geometry and screen efficiency limited detection.^[ref]

John Douglas Cockcroft's 1951 lecture recalls detection at $125\mathrm{kV}$ and an absorption range about $8.4\mathrm{cm}$, then refined alpha particle energies about $8.6\mathrm{MeV}$ each. He places the work under Ernest Rutherford's direction. The inferred nuclear reaction was lithium-7 plus a proton producing two alpha particles.^[ref]

The logic has several independent links. Beam blocking tests whether the flashes depend on bombardment. An absorber tests whether scattered beam particles could reach the screen. A particle range tests product identity and kinetic energy, while coincidences test whether two products belong to one event. These tests support a reaction interpretation jointly; counting flashes alone is not an isotope identification, and a range-to-energy conversion needs calibration. The lithium proton reaction energy below is a modern calculation, separate from those historical measurements.

A hotter stellar core can favor a higher-barrier route despite fewer catalyst nuclei. To isolate this competition, prescribe a local hydrogen burning toy model at fixed mass density $\rho$, with reference $T_0=15\mathrm{MK}$ andChoose $E_{G,pp}=493\mathrm{keV}$ and $E_{G,\mathrm{CNO}}=45000\mathrm{keV}$, rounded barrier parameters for a proton pair and proton capture on nitrogen-14. These prescribe the temperature dependence, while the following freely chosen heating normalization incorporates effective nuclear factors and deposited energy:Here $X$ is hydrogen mass fraction, $X_{\mathrm{CNO}}$ is CNO mass fraction, and ${ϵ}_{\ast }$ is an arbitrary positive unit of stellar energy-generation rate. For $X=0.70$ and $X_{\mathrm{CNO}}=0.01$, the reference ratio is $0.01$ by construction. It is not a measured solar ratio. The CNO cycle bottleneck is represented by one effective rate, without evolving the existing proton-proton chain branches or catalyst network.

At $T_0$, the logarithmic temperature slopes are $({\tau }_{pp,0}-2)/3=3.90$ and $({\tau }_{\mathrm{CNO},0}-2)/3=19.90$. The larger Coulomb barrier gives a steeper fractional response. Because these slopes change with temperature, this example retains the exponential rather than extending two fixed power laws. Writing $R_0=0.01(X_{\mathrm{CNO}}/0.01)(0.70/X)$ and $D={\tau }_{\mathrm{CNO},0}-{\tau }_{pp,0}$ givesprovided the bracket is positive. With the chosen composition, $T_{\ast }=20.30\mathrm{MK}$. Reducing $X_{\mathrm{CNO}}$ to $0.001$ at unchanged $X$ shifts it to $23.91\mathrm{MK}$. For $X_{\mathrm{CNO}}=0$, this catalytic route supplies no heat in this model. These are local toy crossovers: a whole star's luminosity requires integrating its stellar energy-generation rate through its stellar composition profile and stellar structure. Nuclear features, plasma screening and changes of the dominant bottleneck limit the model's extrapolation.

The conjugate acid of a chemical base is the chemical species formed when it accepts one proton. This is a relationship between partners, rather than a claim that the partner is a strong acid.

A conjugate acid-base pair consists of two chemical species related by transfer of one proton. The conjugate acid has one more proton and one more positive unit of electric charge than the conjugate base.

Conjugate addition attacks a beta position in a conjugated electrophile and redistributes pi bonding, often generating an enolate. proton transfer then supplies a saturated carbonyl product.

A conjugate base is what remains after a chemical acid donates one proton. In the conjugate acid-base pair $\mathrm{HA}/{\mathrm{A}}^{-}$, $\mathrm{HA}$ is the conjugate acid of ${\mathrm{A}}^{-}$; accepting a proton reverses the conversion. For example, acetic acid $\mathrm{C}{\mathrm{H}}_3\mathrm{COOH}$ loses a proton to give its conjugate base $\mathrm{C}{\mathrm{H}}_3\mathrm{CO}{\mathrm{O}}^{-}$. Partners differ by one proton and one unit of electric charge; they need not always be neutral and negative. Hydronium/water and water/hydroxide are also conjugate acid-base pairs.

At a prescribed pH, the ideal dilute acid dissociation constant determines the partition of a monoprotic acid inventory between its chemical species:These dimensionless fractions sum to one. They are the weak acid dissociation fraction and its complement when the only acid-bearing chemical species are $\mathrm{HA}$ and ${\mathrm{A}}^{-}$. Equal fractions occur at $\mathrm{pH}=\mathrm{p}{K}_a$ in this ideal approximation. For nonideal chemical solutions, equality of thermodynamic activities need not mean equality of concentrations.

For stipulated pKa $5$, the conjugate base fractions at pH $4$, $5$ and $6$ are $1/11$, $1/2$ and $10/11$. Here an external reservoir sets pH; its ions must supply the additional electric charge balance. The diagram omits those ions and water populations. It does not represent three pure $\mathrm{HA}$ samples at identical analytical concentration with freely chosen pH. In the latter experiment, the weak acid mass and charge balances determine pH as well as the partition.

A cosmic ray is a high-energy charged particle propagating through space. Galactic cosmic-ray electrons emit synchrotron and inverse-Compton radiation, while cosmic-ray nuclei produce gamma rays through collisions with gas.

In modern terminology, a primary cosmic ray arriving at Earth's atmosphere is usually a proton or another atomic nucleus, with an electron component as well. Atmospheric collisions generate secondary cosmic rays and air showers, including muons, electrons and photons. A gamma ray can also initiate an air shower, although it is electrically neutral. Consequently, detecting atmospheric ionization does not establish that an incoming primary cosmic ray passed through the detector. Magnetic fields bend charged particles, while gamma rays provide a more direct directional connection to their sources.^[ref]

The Hess cosmic-ray balloon experiment asks how atmospheric shielding and separation from the ground affect ionization. Its power comes from changing the environment around an enclosed detector instead of identifying each incoming particle.

Combining $r=mv/(|q|B)$ with the classical kinetic energy givesHere $E$ denotes kinetic energy, not relativistic total energy. At fixed magnetic field, twice the final radius allows four times the classical kinetic energy. At fixed final kinetic energy, a larger accelerating gap voltage reduces the number of crossings needed, but does not change the required orbit radius.

For an illustrative proton with $B=1.00\mathrm{T}$ and peak gap voltage $V_0=10.0\mathrm{kV}$, take negligible injection kinetic energy, on-crest kicks, a zero-width gap, and no losses. Each crossing adds $10.0\mathrm{keV}$, so $100$ crossings give $1.00\mathrm{MeV}$, using electronvolts. With $e=1.602176634\times 10^{-19}\mathrm{C}$ and $m_p=1.67262192595\times 10^{-27}\mathrm{kg}$,The $100$th kick arrives after $99$ intervening half-turns, about $3.247\mu \mathrm{s}$ after the first kick in this idealization. The final two curvature radii differ by $r(1\mathrm{MeV})[1-\sqrt{99/100}]\simeq 0.724\mathrm{mm}$. That difference is a curvature-radius increment, not a general formula for separation of real extracted turns: successive arc centers shift, and extraction also depends on focusing and the gap geometry. These chosen settings are a calculation, not historical measurements.

Scattering that resolves the constituents of a hadron at large spacelike momentum transfer, with an inclusive sum over final hadron states.

In electron scattering from a proton, write the reaction as $e^{-}p\to e^{-}X$: the outgoing electron is measured, while $X$ denotes all allowed final hadron states. Large momentum transfer supplies a short-distance probe; a large final invariant mass separates the deep continuum from elastic scattering and individual particle resonances. The useful surprise is that an extended proton can have a response characteristic of much smaller constituents. Deep inelastic scattering turns measurements outside the proton into constraints on its internal parton distribution functions.

The SLAC-MIT deep inelastic electron scattering experiment connects this definition to an actual measurement. Its evidence came from distributions of outgoing electron energies and scattering angles, rather than a photograph of a quark. Bjorken scaling concerns deep-inelastic structure functions after known scattering factors have been accounted for; it does not say that the raw differential scattering cross-section is constant.

Deprotonation removes a proton from a chemical species, changing its electric charge by $-1$. It can expose a donor lone pair or change donor charge without changing the metal oxidation state.

This stable hydrogen isotope has one proton and one neutron. In the Proton–proton chain it is produced by the slow weak proton-pair reaction and is rapidly consumed by proton capture to make helium-3. Its short nuclear lifetime inside a stellar core allows a deuterium quasi-equilibrium in proton-proton burning approximation.

deuterium proton capture is much faster than the weak reaction that produces deuterium. Its abundance therefore adjusts so that ${\lambda }_{21}{n}_2{n}_1\simeq {\lambda }_{11}{n}_1^2/2$. Substituting this balance eliminates the fast intermediate from the slower proton and helium-3 evolution equations. This is a quasi-steady approximation, not an assumption that hydrogen itself is in nuclear equilibrium.

The bound atomic nucleus containing one proton and one neutron. Its ground-state spin is one and its isospin is zero. The appropriately quantized toroidal two-Skyrmion models these quantum numbers.

Diisopropylethylamine is a sterically hindered tertiary amine base. It can remove protons and trap acid while competing relatively weakly as a nucleophile.

Dimethyl sulfoxide is a polar aprotic solvent. It supports reactions of anions with many organic electrophiles without providing an O–H proton.