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Reduction using hydrogen and a catalyst. Selectivity depends on the catalyst, pressure, solvent and functional groups: reducing an alkene while retaining a ketone is a distinct requirement from reducing a nitrile while retaining an ester.

Walther Bothe and Herbert Becker observed penetrating radiation from beryllium struck by alpha particles before James Chadwick's interpretation.^[ref]

Irène Joliot-Curie and Frédéric Joliot found that adding material containing hydrogen increased ionization, interpreting the ejected protons as Compton scattering recoils from extremely energetic gamma rays. James Chadwick tested this interpretation against nuclear recoils in other elements.^[ref]

The counter coupled a small ionization chamber to an amplifier and oscillograph: charged particles produced ions, and the electrical signal gave a deflection. With Norman Feather, James Chadwick also observed nitrogen recoil tracks in a cloud chamber.^[ref]

The apparatus used polonium on silver facing beryllium inside an evacuable vessel. Paraffin wax before the aluminium counter window supplied recoil protons; intervening aluminium screens measured their particle range. Deflections were photographed on bromide paper. The first counter contained air; later fillings included hydrogen, helium, nitrogen, oxygen and argon. Counts with wax absent included gas recoils; wax insertion added entering protons. Thick lead between source and counter hardly changed the initial counts, testing penetration against the low background.^[ref]

The diagram separates two routes to a signal: a proton entering from the wax and a nuclear recoil created inside the chamber gas. Its lower row is a logical summary, rather than a reconstructed experimental trace. In either route the observed ionization belongs to a charged secondary particle; identifying the incident radiation requires an additional collision model.

In the February letter, a photon interpretation requiring about $52\mathrm{MeV}$ for the protons predicted only about $0.4\mathrm{MeV}$ for nitrogen recoils, below the observed ionization. Here $1\mathrm{MeV}=10^6$ electronvolts. James Chadwick proposed a neutral particle near the proton mass and the nuclear reactionThese are the letter's approximate historical values, not a modern mass determination.^[ref]

Why compare two materials? A gamma ray is a photon, so its incident momentum is $E_{\gamma }/c$, where $c$ is the speed of light. A slow massive projectile instead has momentum $mv$ and kinetic energy $m{v}^2/2$. The relationship between incoming momentum and energy therefore changes. An elastic collision model must explain the recoil endpoints for both target masses with the same incident projectile population. Calling the radiation neutral supplies no such agreement by itself.

The original measurements depended on particle range calibration, material in the path, detector response and whether a recoil was fully stopped in the sensitive gas. Large deflections alone need not specify a complete recoil energy. The calculations below expose the ideal collision assumptions behind the inference; applying them to a measured spectrum requires checking those assumptions.

Chain-growth termination removes the ability of a reactive chain carrier to continue the succession of growth steps.^[ref] Two illustrative outcomes have different molecule counts:The first joins the two chains into one inactive polymer molecule. The second leaves two inactive polymer molecules, as can occur when one chain end transfers hydrogen to the other instead of their ends joining. End-group chemistry is suppressed in these unit-count symbols; they are not complete molecular formulas. Losing two polymerization-active sites does not mean losing two chains or any incorporated monomeric units. A temporarily inactive, reactivatable site must not be counted as irreversible chain-growth termination.

A chemical bond associates chemical atoms or groups of chemical atoms into a sufficiently stable structure to treat it as a distinct entity. The concept covers connections within molecules and in extended solids; see the IUPAC Gold Book, chemical bond. It is useful because composition alone does not specify how the chemical atoms are connected, and those connections help determine a chemical substance's properties and possible chemical reactions.

In a covalent bond, electrons are shared between chemical atoms. Two hydrogen chemical atoms can form a molecular hydrogen molecule, with its electrons interacting with both atomic nuclei. In the usual description of this diatomic molecule, the potential energy as a function of nuclear separation has a minimum: moving the nuclei too close or too far raises the energy. See 7.2 Covalent Bonding.

Separating bonded chemical atoms requires energy; forming the corresponding chemical bonds releases energy. Whether an overall chemical reaction releases energy depends on both the chemical bonds broken and those formed. The lines in the stoichiometry diagram indicate connections schematically, rather than literal rods or a sequence of microscopic events.

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.

A chemical equation represents a chemical reaction using chemical formulas, with reactants on the left and reaction products on the right. A balanced chemical equation has the same number of chemical atoms of each chemical element on both sides. For molecular hydrogen and molecular oxygen forming water,The coefficients $2,1,2$ give the relative numbers of molecules; the coefficient $1$ is normally omitted. Count hydrogen as $2\times 2=4$ on the left and $2\times 2=4$ on the right, and oxygen as $1\times 2=2$ on the left and $2\times 1=2$ on the right. See Flowers et al., Chemistry 2e, §4.1: writing and balancing chemical equations.

To balance the initial expression ${\mathrm{H}}_2+{\mathrm{O}}_2⟶{\mathrm{H}}_2\mathrm{O}$, first put $2$ before water to match the two oxygen chemical atoms. This creates four hydrogen chemical atoms on the right, so put $2$ before molecular hydrogen. Changing a coefficient multiplies the entire chemical formula. Changing a subscript changes composition and usually the chemical substance: $2{\mathrm{H}}_2\mathrm{O}$ is two water molecules, whereas ${\mathrm{H}}_2{\mathrm{O}}_2$ is one hydrogen peroxide molecule. Never balance a chemical equation by changing its subscripts.

The bookkeeping follows from conservation of the atomic nuclei in ordinary, non-nuclear chemical reactions; chemical bonds and the distribution of electrons can change. For a chemical equation involving ions, total electric charge must also match. For example, the existing self-ionization of water equation has zero total electric charge on each side, since the $+1$ of hydronium cancels the $-1$ of hydroxide. See 2.6 Ionic and Molecular Compounds (§2.6: nuclei and ions).

The same $2:1:2$ ratio relates changes in amount of substance: two moles of molecular hydrogen consumed per mole of molecular oxygen correspond to two moles of water formed. A mole is a defined unit, not one molecule; the little whole-number picture is an abstract counting model, not a claim that a macroscopic sample contains just five molecules. See molecular count and amount of substance for the exact conversion and SI base unit: mole by Bureau International des Poids et Mesures for the definition.

This is why a balanced chemical equation is useful: stoichiometry turns the same atom accounting into relations between measurable quantities. It does not determine reaction rate, the final conversion set by chemical equilibrium, or the actual yield of recovered reaction products. The limiting reagent gives an upper bound under the specified chemical reaction.

A chemical formula uses symbols of chemical elements and numerical subscripts to record composition. In the molecular formula ${\mathrm{H}}_2\mathrm{O}$ of water, the subscript $2$ counts two hydrogen chemical atoms, and the omitted subscript after $\mathrm{O}$ means one oxygen chemical atom. A molecular formula describes one molecule; a chemical formula need not describe a discrete molecule.

Read a preceding coefficient separately from the subscripts. One ${\mathrm{H}}_2\mathrm{O}$ contains two hydrogen and one oxygen chemical atom; $2{\mathrm{H}}_2\mathrm{O}$ contains four hydrogen and two oxygen chemical atoms distributed between two water molecules. In ${\mathrm{H}}_2{\mathrm{O}}_2$, the second subscript instead puts two oxygen chemical atoms into each hydrogen peroxide molecule. Thus $2{\mathrm{H}}_2\mathrm{O}\ne {\mathrm{H}}_2{\mathrm{O}}_2$: the coefficient scales the whole chemical formula, while a subscript specifies its composition. See Flowers et al., Chemistry 2e, §2.4: chemical formulas.

For crystalline $\mathrm{NaCl}$, the chemical formula specifies a $1:1$ ratio of sodium ions ${\mathrm{Na}}^{+}$ to chlorine ions ${\mathrm{Cl}}^{-}$. Its formula unit is the accounting entity; the ordinary crystal is an extended arrangement of ions, rather than a collection of discrete $\mathrm{NaCl}$ molecules. Specifying the entity matters when assigning an amount of substance. See formula unit and 2.6 Ionic and Molecular Compounds (§2.6: ionic and molecular compounds).

A molecular formula gives an atom inventory, not the full arrangement of chemical bonds or the molecular geometry. For example, ${\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6$ counts six carbon, twelve hydrogen, and six oxygen chemical atoms in a glucose molecule, but does not specify the pattern shown by its Fischer projection. Different structures can share a molecular formula. This compact inventory is useful for chemical equation accounting precisely because it leaves the structural detail to other representations.

The choice of letters has an early explanation in Jöns Jacob Berzelius, Essay on the Cause of Chemical Proportions (1813–1814), §III, transcribed by Carmen Giunta: letters made chemical signs easier to write and print, and formulas compressed information about composition. His numerical notation differed from modern subscripts; the lasting idea was to make proportions readable in ordinary text.

A chemical reaction interconverts chemical species, as defined by the ^[ref]. The consumed species are reactants; the formed species are reaction products. In ordinary chemical reactions, chemical atoms are rearranged while each chemical element's total atom count is conserved. For a complete chemical equation, net electric charge is conserved too.

For example, the balanced chemical equationdescribes conversion of molecular hydrogen and molecular oxygen into water. Both sides contain four hydrogen chemical atoms and two oxygen chemical atoms. Three reactant molecules become two reaction product molecules: atom counts are conserved, but molecule counts need not be. See Flowers et al., Chemistry 2e, balancing chemical equations.

The coefficients describe net consumption and formation, without asserting that three molecules collide in one step. A balanced chemical equation supplies quantitative constraints; it does not determine how quickly the chemical reaction occurs, or whether chemical equilibrium prevents complete conversion. Those questions need further information. Keeping these roles distinct makes stoichiometry useful even when the microscopic details are complicated.

Chemistry connects the composition and structure of chemical substances to their properties and transformations. Its central surprise is that rearranging the same chemical atoms can produce a different substance: molecular hydrogen and molecular oxygen can become water without changing which chemical elements are present. Chemical bonds explain the connections; chemical reactions describe the transformations; stoichiometry makes quantitative predictions from the bookkeeping.

This gives a useful route from an invisible world to measurable quantities. A molecule has a definite composition, such as two hydrogen chemical atoms and one oxygen chemical atom in water. A sample contains an enormous number of such molecules. Counting them through amount of substance, measured in moles, lets the same small-number ratios describe a macroscopic sample. The beauty is that the bookkeeping survives this huge change of scale.

A compound composed of carbon, chlorine and fluorine, with no hydrogen. Many such fully halogenated molecules resist lower-atmospheric attack but release reactive chlorine after stratospheric photodissociation, contributing to catalytic ozone destruction.

Citrate denotes an ion derived from citric acid. The commonly specified form has electric charge equal to that of three electrons and chemical formula ${\mathrm{C}}_6{\mathrm{H}}_5{\mathrm{O}}_7^{3-}$; it results from removing three hydrogen ions from citric acid. Forms with additional hydrogen ions attached through protonation also occur. ^[ref]

A closed deltahedral carborane. Thermal conversion of nido precursors may change hydrogen content or cage size as well as carbon positions.

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.

For homologous, chemically uniform, gas-pressure-supported radiative stars with specific energy generation $ϵ\propto X\rho T^{13}$ and composition-dependent constant opacity, stellar homology gives $L_{\mathrm{nuc}}\propto X{\mu }^{13}{M}^{15}{R}^{-16}$ and $L_{\mathrm{rad}}\propto {\mu }^4{M}^3/\kappa$. Equating them gives the displayed scalings. Hydrogen depletion changes both mean molecular weight and electron-scattering opacity; holding composition fixed gives $R\propto M^{3/4}$ and $L\propto M^3$. The power-law burning approximation applies only while hydrogen fuel remains.

A covalent bond joins chemical atoms through shared electrons. In the familiar two-centre description, one bond pair contributes to a connection between two atomic nuclei. Sharing means that the electrons belong to the combined arrangement and interact with both atomic nuclei; it does not mean that identifiable dots shuttle along drawn paths. The ^[ref] emphasizes the concentration of electrons between atomic nuclei and the resulting attraction and characteristic separation. The pair picture is especially useful for simple molecules, but is not a universal description of every covalent bond.

A Lewis structure turns this picture into practical bookkeeping. Count the valence electrons, indicate which chemical atoms are connected, and allocate two electrons to each line. A bond pair is shared; a lone pair is assigned to one chemical atom without connecting it to another. A double line represents two bond pairs. Dots and lines record allocations, rather than positions, trajectories, or a measured three-dimensional arrangement. ^[ref]

For molecular hydrogen, ${\mathrm{H}}_2$, each neutral hydrogen chemical atom supplies one valence electron. Thus $1+1=2$ valence electrons make one bond pair, represented by $\mathrm{H}-\mathrm{H}$, with no lone pairs. Each hydrogen counts the same shared pair when checking its two-electron arrangement. The molecule still contains two electrons, not four: counting a pair around both endpoints does not create extra electrons.

For water, ${\mathrm{H}}_2\mathrm{O}$, neutral oxygen supplies six valence electrons and the two hydrogen chemical atoms supply one each: $6+1+1=8$. Two O–H connections consume four electrons as two bond pairs. The remaining $8-4=4$ electrons form two lone pairs on oxygen. Around oxygen, the two bond pairs and two lone pairs count as eight electrons; each hydrogen counts two. The whole water molecule has ten electrons, because two additional oxygen electrons are omitted from this valence electron drawing.

For ammonia, ${\mathrm{NH}}_3$, the total is $5+3\times 1=8$ valence electrons: five from nitrogen and three from hydrogen. Three N–H connections use six electrons as three bond pairs, leaving two electrons as one lone pair on nitrogen. Thus water and ammonia have the same total of eight valence electrons but different allocations: two plus two pairs versus three plus one. This small calculation already distinguishes their connectivity without a detailed quantum mechanics calculation.

For molecular oxygen, ${\mathrm{O}}_2$, $6+6=12$ valence electrons give the conventional $\mathrm{O}=\mathrm{O}$ Lewis structure. Its two bond pairs use four electrons, leaving eight as four lone pairs, two on each oxygen. Each oxygen consequently counts eight electrons locally. However, actual molecular oxygen has two unpaired electrons and exhibits paramagnetism: it is attracted into a stronger magnetic field. The all-paired Lewis structure cannot capture this observation. Molecular orbital theory describes the unpaired electrons; the successful counting diagram alone is insufficient. ^[ref]

Why does sharing produce a stable separation? For molecular hydrogen, the electronic arrangement responds as the atomic nuclei approach. Their interactions can lower the energy, but pushing them too close raises it. A curve of potential energy against separation therefore has a local minimum, rather than falling forever. Attraction and repulsion balance there. This is a statement about the combined system, not a claim that stationary electrons sit between otherwise motionless atomic nuclei. ^[ref]

The following Morse potential makes those features calculable. Set $x=r/r_e$, where $r$ is separation and $r_e$ its equilibrium value, and let $D$ be the well depth. With the self-chosen parameter $a=2$, define the dimensionless quantitiesHere $F=-dV/dr$ is the net separating force, obtained from the derivative of the potential energy. Positive $f$ pushes the chemical atoms apart; negative $f$ draws them together. These are illustrative curves with $r_e=D=1$ in chosen units, not measured molecular hydrogen data or fitted parameters.

At $x=1$, $u=-1$ and $f=0$. The second derivative is $u^{\prime \prime }(1)=8>0$, confirming a local minimum. At $x=0.5$, $u=(1-e{)}^2-1\approx 1.9525$; at $x=1.5$, $u=(1-e^{-1}{)}^2-1\approx -0.6004$. As $x$ increases without bound, $u$ approaches zero from below. Thus moving from the well bottom to separated chemical atoms requires an increase of $D$ in this model's potential energy. An actual quantum mechanics dissociation threshold also depends on the initial motion of the atomic nuclei, so the well depth alone is not every measured dissociation energy.

The force panel separates $f$ into a positive term $4e^{-4(x-1)}$ and a negative term $-4e^{-2(x-1)}$. At $x=1$ they are $+4$ and $-4$, cancelling exactly; nearer separations favour the positive term. These are algebraic components of the chosen Morse potential, not separately measured microscopic forces. Their usefulness is to show how a balance arises from the slope of one energy curve.

The beauty of the pair picture is its economy: a few marks summarize connectivity and constrain what a proposed molecule can contain. Its historical anchor is Gilbert N. Lewis's 1916 paper ^[ref], also available as an ^[ref]. Lewis structures remain useful because they answer counting questions quickly; quantum mechanics supplies the richer account when energy, shape, or unpaired electrons matter.

In the usual DNA context, deoxyribose means 2-deoxy-D-ribose, a five-carbon monosaccharide with molecular formula ${\mathrm{C}}_5{\mathrm{H}}_{10}{\mathrm{O}}_4$. Relative to D-ribose, the hydroxy group at C2 is replaced by hydrogen. The locant 2 matters: it identifies which position loses its oxygen. See Favre and Powell, IUPAC Blue Book, P-102.5.3: deoxy sugars and IUPAC: nucleic acids and their component sugars.

The paired Fischer projections in ribose make the change concrete. C2 has hydrogen on both sides, while C3 and C4 retain their hydroxy groups on the right. C2 is therefore not a stereocenter: exchanging its two identical hydrogen substituents cannot produce a distinct configuration. The unchanged C3 and C4 still carry stereochemical information.

Replacing $\mathrm{OH}$ by $\mathrm{H}$ removes one oxygen but leaves the total hydrogen count unchanged: the hydrogen belonging to the removed hydroxy group is replaced by a hydrogen bonded directly to carbon. Thus ${\mathrm{C}}_5{\mathrm{H}}_{10}{\mathrm{O}}_5$ becomes ${\mathrm{C}}_5{\mathrm{H}}_{10}{\mathrm{O}}_4$. This comparison describes structures, rather than a complete chemical reaction or its mechanism.

In DNA, deoxyribose is incorporated as a ring in each nucleotide, with phosphate connections building the backbone. Its C2′ bears hydrogen where RNA's ribose bears a hydroxy group. This small local difference lets the sugar structure identify the two kinds of nucleic acid; the nucleobases supply their sequence information. See Alberts et al.: nucleotides as the subunits of DNA and RNA.

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.

Oxygen-directed anti addition of aluminium and hydrogen across an alkyne, giving a stereodefined vinylaluminium species.

In On the Constitution of Atoms and Molecules, Part I (1913), pp. 8–9, Niels Bohr interprets existing hydrogen discharge and astronomical spectra. Electrical discharge in a vacuum tube removes electrons; recombination supplies spectral lines. This is a theoretical interpretation, without a reported spectrograph of his own.^[ref]

An actual optical obstacle appears in Theodore Lyman's measurements: hydrogen discharge light entered an evacuated spectrograph directly through a slit, avoiding a transmitting window. A concave reflection diffraction grating dispersed the light onto photographic film. Pumping preserved the vacuum; a second slit supplied a known spectral displacement for wavelength calibration. Gas contamination and vacuum leaks limited the measurement. This apparatus resolved ultraviolet spectral lines; it did not image orbits.^[ref]

For a separate original calibration exercise, suppose an idealized spectrograph returns synthetic vacuum line positions $x_n={\lambda }_{n\to 2}+b$ for $n=3,4,5,6$, with chosen additive offset $b=0.200\mathrm{nm}$. Assume its dispersion scale is already known and only this offset is uncertain. Compare the finite-mass prediction with the fixed-nucleus prediction ${\lambda }_n^{(\infty )}=(\mu /m_e){\lambda }_{n\to 2}$. Calibrate each model using only the $3\to 2$ line: $\hat{b}=x_3-{\lambda }_3^{\mathrm{model}}$. Then hold that offset fixed and test the other lines with residualsFor the finite-mass model every $d_n=0$. The fixed-nucleus model has $\hat{b}=0.55733\mathrm{nm}$ and residuals $d_4=-0.09264\mathrm{nm}$, $d_5=-0.12100\mathrm{nm}$, $d_6=-0.13400\mathrm{nm}$. Algebraically $d_n=(1-\mu /m_e)({\lambda }_n-{\lambda }_3)$: one additive calibration cannot absorb a multiplicative change of the wavelengths. Allowing an unknown multiplicative dispersion factor as well would make the two models degenerate in this exercise, so independent scale calibration matters.