Codex @codex  0

The chemical element with atomic number 12. Magnesium isotopes occur among products of carbon burning and alpha-capture neutron-source reactions.

For a modern chosen example, the National Institute of Standards and Technology lists neutral magnesium atomic masses $23.985041697\mathrm{u}$, $24.985836976\mathrm{u}$, and $25.982592968\mathrm{u}$, with reference isotopic abundances $0.7899$, $0.1000$, and $0.1101$. They describe the isotopes with mass numbers 24, 25, and 26, respectively.^[ref] These modern inputs are not a reconstruction of historical observations.

Use the dimensionless mass-to-charge ratio coordinate $x=(m/\mathrm{u})/z$. For the illustration only, approximate ion masses by the neutral atomic masses. The singly charged positions are then near $23.98504$, $24.98584$, and $25.98259$; the doubly charged companions are near $11.99252$, $12.49292$, and $12.99130$. The neutral-to-ion correction already given above is essential at higher accuracy. A peak near $x=12$ alone need not identify a chemical element: another ion with a different electric charge can occupy the same mass-to-charge ratio interval.

For the narrow singly charged peak at $x\approx 24.98584$, the chosen full width at half maximum $\Delta x=0.12$ gives mass resolving power $R\approx 208.2$; widening to $\Delta x=1.20$ gives $R\approx 20.82$. Adjacent isotope spacings here are approximately one unit in $x$. Peaks are visibly separated in the first chosen profile and overlap strongly in the second. A small uncertainty in a fitted peak centre would not by itself make the overlapping components resolved.

Even integrated peak areas need a response model. For isotope fraction $f_i$, let ${\eta }_{i,z}$ collect the probability of ionization into electric charge state $z$, transmission through the analyzer, and the detection response. In a linear instrument with overall exposure factor $C$, the component area isEqual ${\eta }_{i,z}$ at a fixed $z$ makes normalized areas equal the fractions; otherwise it does not. In the chosen example, doubling only the mass-25 response changes the normalized areas to $0.71809$, $0.18182$, and $0.10009$, although the neutral sample is unchanged. Photographic darkening introduces another possible nonlinearity: neither line darkness nor peak height is a universal measure of neutral isotopic abundance. Calibration of position and calibration of intensity answer different questions. Matched standards, a known electric charge assignment, and a response correction make isotope analysis useful; a visually impressive set of peaks alone does not supply those controls.

A mass spectrometry instrument with a photographic readout. In the 1919 apparatus described in Chapter V: The Mass-Spectrograph, a gas discharge produced positive ions. Two narrow slits formed a ribbon beam in a vacuum; plates applied an electric field to spread it, an aperture selected part of it, and a magnetic field bent it oppositely. Focusing reduced the spread caused by differing ion speeds, concentrating a given mass-to-charge ratio into a line on a photographic plate.

The observed quantity was line displacement from a fiducial spot. Known reference lines calibrated displacement against mass-to-charge ratio; repeated exposures with changed magnetic field tested the calibration. Evacuation limited collisions. Comparing line shapes with narrow and wide apertures helped distinguish geometric broadening from photographic spreading. Finite slit widths, plate response, and overlapping molecular or multiply charged ions limited interpretation. See Chapter V: The Mass-Spectrograph (§§33–40: apparatus and photographic procedure; §§43 and 45–46: calibration, aperture comparisons, and accuracy).

In Mass spectra and isotopes by Francis William Aston (Nobel lecture, 12 December 1922), the reported neon lines at 20 and 22 have companions at 10 and 11 from doubly charged ions. That paired pattern and comparison with reference lines support different atomic masses within one chemical element, rather than an atomic mass concentrated at the bulk average. The lecture also describes an earlier failed separation by distillation and partial separation by diffusion, showing why the focused mass spectrum supplied stronger evidence. These numbers used a historical oxygen-based reference scale. The lecture's whole-number rule was an empirical approximation at its stated accuracy, not the modern exact definition $A=Z+N$.^[ref]

Mass spectrometry separates and detects ions according to mass-to-charge ratio. It can distinguish isotopes which belong to the same chemical element but have different atomic masses. The instrument measures ions: interpreting the result as a neutral atomic mass requires accounting for electron removal and its ionization energy. For a singly positive ion in its ground state, $m_{+}=m_{\mathrm{a}}-m_e+I/c^2$, where $m_e$ is the electron rest mass, $I$ is the ionization energy, and $c$ is the speed of light.

For a simple illustrative analyzer, positive ions of mass $m$ and electric charge $q=ze$ gain kinetic energy $qV=m{v}^2/2$ across an electric potential difference $V$ before entering a transverse uniform magnetic field $B$. The Lorentz force supplies centripetal acceleration, soAt fixed $V$ and $B$, the measured bending radius $r$ separates mass-to-charge ratios, not masses independently of electric charge. This ideal model assumes negligible initial kinetic energy and speeds small compared with the speed of light; the historical focusing mass spectrograph used the geometry described below.

The experimental achievement is to turn invisible differences between individual ions into separated, calibrated positions. Aston velocity focusing explains how an early mass spectrograph sharpened its images; the velocity-selected magnetic mass analyzer provides an independent model whose equations can be checked directly. The magnesium isotope mass spectrum shows why position, width, and intensity carry different information.

The abundance of chemical elements heavier than helium in astronomical material. A metal mass fraction measures their combined mass; spectroscopic abundance ratios are other measures of metallicity and need not be numerically identical to that fraction.

The fraction of total mass in chemical elements heavier than helium, so the hydrogen mass fraction, helium mass fraction and metal mass fraction satisfy $X+Y+Z=1$. Despite the astronomical name, this includes elements such as carbon and oxygen that are not chemical metals.

A molecular formula gives the number of chemical atoms of each chemical element in a molecule. For urea, ${\mathrm{CH}}_4{\mathrm{N}}_2\mathrm{O}$ counts one carbon, four hydrogen, two nitrogen and one oxygen chemical atom. It records composition rather than the arrangement of chemical bonds.

A molecule, using the International Union of Pure and Applied Chemistry (IUPAC) convention, is an electrically neutral entity containing two or more chemical atoms. Its constituents form a bound unit through chemical bonds; merely drawing a boundary around neighboring particles does not make a molecule. The neutrality requirement concerns total electric charge, not the absence of internal charge separation: water is a polar molecule with zero total electric charge.^[ref]

One water molecule, ${\mathrm{H}}_2\mathrm{O}$, contains two hydrogen and one oxygen chemical atom. One molecular oxygen molecule, ${\mathrm{O}}_2$, contains two oxygen chemical atoms; a molecule need not contain different chemical elements. One carbon dioxide molecule, $\mathrm{C}{\mathrm{O}}_2$, contains one carbon and two oxygen chemical atoms. The molecular formula records these inventories, while molecular geometry describes their arrangement. Water and carbon dioxide are chemical compounds; molecular oxygen is a form of one chemical element.

Ordinary crystalline sodium chloride, $\mathrm{NaCl}$, contains an extended arrangement of sodium cations $\mathrm{N}{\mathrm{a}}^{+}$ and chlorine anions $\mathrm{C}{\mathrm{l}}^{-}$. Its formula unit specifies one of each for compositional accounting, without selecting a unique isolated pair. Bulk neutrality therefore does not imply a material consists of neutral molecules. This statement concerns the ionic crystal; the physical state and conditions matter when deciding what particles a chemical formula represents.^[ref]

A polyatomic ion is a charged bound group of chemical atoms, such as hydronium, ${\mathrm{H}}_3{\mathrm{O}}^{+}$. A molecular ion formed by removing an electron from intact water, ${\mathrm{H}}_2{\mathrm{O}}^{\bullet +}$, retains the same atom inventory but has net electric charge $+e$. Neither satisfies the neutral-molecule definition. Distinguishing these entities makes molecular count and amount of substance and mass spectrometry interpretable: say whether the count is of chemical atoms, neutral molecules, ions, or formula units.

The useful surprise is that a molecule can be treated as one particle for motion and counting while retaining internal structure. Its molar mass connects a particle inventory to bulk mass; molecular rotation and molecular vibration reveal internal organization. The continuum approximation uses bulk fields in place of individual molecular positions and motions.

The chemical element with atomic number 10. Neon burning uses photodisintegration and alpha capture, while neon-22 can provide neutrons through ${}^{22}\mathrm{Ne}(\alpha ,n){}^{25}\mathrm{Mg}$.

Neptunium is the chemical element with atomic number 93. Its isotope neptunium-239 occurs between uranium-239 and plutonium-239 in a neutron-capture and beta decay production chain.

The number of neutrons in an atomic nucleus. Two isotopes of the same chemical element differ in neutron number while sharing an atomic number.

The chemical element with atomic number 28. Radioactive nickel-56 is produced in explosive burning; the nickel-56 decay chain contributes energy to supernova emission.

Lord Rayleigh received the award for gas-mass density investigations and the discovery of argon.^[ref] The Rayleigh-Ramsay argon density experiment shows how a small reproducible density discrepancy can reveal a new chemical element.

Awarded to Charles Glover Barkla for characteristic X-rays of the chemical elements; he received it in 1918. The Barkla characteristic X-ray experiment describes the experimental separation of components.^[ref]

One half went to Subrahmanyan Chandrasekhar for theoretical studies of processes governing stellar structure and evolution. The other half went to William Alfred Fowler for theoretical and experimental studies of nuclear reactions involved in forming the chemical elements in the universe.^[ref]

A chemical element in group 18 of the periodic table. Argon is a familiar example: its chemical inertness under many ordinary conditions makes it useful when a process needs a gas that does not readily react with the material being processed. Chemical inertness is a statement about conditions, rather than an assertion that no compound can exist.

Static fluctuations in which chemical element occupies a site produce scattering beyond coherent Bragg diffraction from the mean crystal structure. For independent binary occupations with probabilities $p$ and $1-p$, the variance of the site's atomic scattering factor is $p(1-p)|f_A-f_B{|}^2$. Writing each site amplitude as its mean plus a zero-mean fluctuation shows that the mean squared total amplitude is the coherent contribution plus a term proportional to the number of sites and this variance. Consequently a forbidden reflection of the average crystal structure can still sit on a diffuse background. Correlated occupations add nontrivial scattering vector dependence.

The octet rule is a useful empirical guide: many Lewis structures of chemical compounds containing carbon, nitrogen, and oxygen give each of those chemical atoms eight electrons when nonbonding electrons and all incident bonding electrons are counted. Hydrogen instead normally counts two electrons. These are local counts, not independent budgets: a shared bond pair counts at both endpoints but only once in the molecule's valence electron total.

In water, oxygen counts $4+4=8$ electrons; in ammonia, nitrogen counts $2+6=8$; in $\mathrm{O}=\mathrm{C}=\mathrm{O}$, carbon counts $0+8=8$ and each oxygen counts $4+4=8$. The charge-separated carbon dioxide drawing also satisfies the octet rule, so the octet rule alone cannot select the dominant contributor. Formal charge provides another check.

The octet rule is a heuristic rather than a theorem about every chemical bond. Odd valence electron totals cannot be partitioned entirely into electron pairs, and some valid Lewis structures have fewer or more than eight electrons around a chemical atom. See Chemistry 2e, 7.3: exceptions to the octet rule. The capacity of the $s$ and $p$ electron subshells, $2+6=8$, helps motivate the guide for these chemical elements, but does not prove universal compliance. Lewis discussed a stable outer group of eight, together with a two-electron arrangement for hydrogen, in The Atom and the Molecule (1916), pp. 768 and 774.

The standard enthalpy of formation is the enthalpy change on forming exactly one mole of the specified compound in its stated standard state from its constituent chemical elements in their reference states at the same specified temperature. The reference states are normally the stable elemental forms at the standard pressure. A standard state does not itself mean 298 K; temperature must be stated separately.

Carl Wilhelm Scheele and Joseph Priestley independently prepared and investigated the gas now called oxygen; Antoine Lavoisier was central to interpreting it within a new account of combustion and chemical composition. Assigning a unique discoverer requires deciding whether discovery means first preparation, first public report, recognition of a distinct kind of gas, or a successful theoretical interpretation. The historical controversy is largely about why one of these achievements should be privileged over the others.

Carl Wilhelm Scheele's investigations, generally dated to the early 1770s, preceded publication of Chemical Treatise on Air and Fire by Carl Wilhelm Scheele in 1777. His work distinguished the component that sustained burning from the remainder of ordinary air. He obtained the active component through several chemical preparations, including heating suitable substances, and interpreted the results in terms of phlogiston. Delayed publication matters to public priority, but it does not show that the experimental work had not occurred. Equally, a publication date alone does not establish the precise date of every earlier trial.^[ref]

Joseph Priestley's 1775 account is unusually revealing because it records hesitation and revision. On 1 August 1774 he heated red mercury(II) oxide with a large burning lens and collected the released gas. A candle burned particularly strongly in it; later trials involving animals and comparison with nitric oxide helped him distinguish its properties from ordinary air. He initially lacked a settled understanding of what he had obtained. Calling the product dephlogisticated air eventually made it intelligible within his own framework: it had an unusually great capacity to accept the phlogiston supposedly released in burning and animal breathing.^[ref]

The modern chemical equation,is a useful reconstruction, but it must not be passed off as Joseph Priestley's own explanation. In modern terms, heating decomposes mercury(II) oxide into mercury and molecular oxygen. The eighteenth-century experimenter instead worked with such categories as calces and differently modified airs. The material operation can be recognized across the change in theory while the meaning of its product remains historically contested.

Antoine Lavoisier made a different contribution. His programme tracked what entered and left substances in calcination and combustion, placing gases within quantitative material balances. In the mercury experiment described in Elements of Chemistry by Antoine Lavoisier, a retort communicated with an enclosed supply of air over mercury. Prolonged heating formed a red calx and diminished the enclosed air. Stronger heating of the recovered calx released an especially combustion-supporting gas; adding it back to the residual air restored the properties of the original mixture. The persuasive feature was the linked decomposition and reconstruction, not just a single spectacular flame.^[ref]

That sequence supported the claim that air was a mixture and that calcination involved combining a metal with part of it. A metal could gain mass because material entered it from the air, without requiring an invisible substance to leave with anomalous properties. Conservation of mass made the weighing scale a constraint on the explanation. However, Antoine Lavoisier's entire system was not modern chemistry. He treated caloric as an explanatory principle and associated the newly named oxygen with the formation of all chemical acids. The latter universal claim is false: hydrochloric acid is an chemical acid whose solute, hydrogen chloride, contains hydrogen and chlorine but no oxygen. This concrete counterexample prevents us from defining discovery as possession of today's complete theory.^[ref]

There are consequently several legitimate allocations of credit. An investigator concerned with earliest preparation may emphasize Carl Wilhelm Scheele; one concerned with the well-documented 1774 experiment and its rapid communication may emphasize Joseph Priestley; one concerned with the explanatory reconstruction of combustion may emphasize Antoine Lavoisier. The last achievement depended on experimental results that the others had produced. Correct interpretation was neither a substitute for preparing the material nor an achievement wholly independent of communication between investigators.

Historians disagree because their accounts embody different pictures of scientific change. A simple accumulation story can make discovery look like identifying one additional item in a ready-made list of chemical elements. A conceptual-change story emphasizes that the list and its criteria were themselves changing: oxygen was not just another variety of modified air in the new chemistry. National priority narratives and the dramatic reputation of the Chemical Revolution can further encourage a single heroic winner. Yet replacing that winner with a collective label is insufficient unless the different experimental and theoretical contributions are explained.

The most defensible answer distributes credit while specifying the achievement. Carl Wilhelm Scheele and Joseph Priestley deserve independent experimental discovery credit; Antoine Lavoisier deserves central credit for the chemical interpretation and reorganization that gave oxygen its place in a new system. Discovery was a sequence of preparation, discrimination, communication and reinterpretation, rather than one instantaneous encounter with a theory-free fact.