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Charles Glover Barkla's 1911 paper describes irradiating a target with an X-ray tube and observing secondary X-rays using an electroscope. For soft Characteristic X-rays from tin, he used a soft primary beam and placed the electroscope close to the target to limit loss in air. Successive aluminium absorbers changed the gas-ionization signal. Thick absorbers suppressed the soft component; a carbon radiator supplied a comparison for the surviving scattered component. Subtracting this estimated contribution left approximately equal fractional losses through successive sheets, evidence for a nearly homogeneous component. Changing primary-beam hardness could suppress excitation of the more penetrating characteristic component.^[ref]

An electroscope reads loss of stored electric charge; ionization in its detecting gas enables discharge. An ionization chamber with an electrometer instead measures the collected electric charge or electric current. These are integrating readouts: neither directly assigns an energy to each arriving photon. The diagram separates these functions without claiming a surviving apparatus drawing.

The K and L components were distinguished by their penetrating power and dependence on the emitting chemical element. Barkla's Nobel lecture, delivered on 3 June 1920 for the 1917 prize, explains that absorber-defined K radiation had seemed homogeneous, whereas later diffraction experiments resolved neighbouring spectral lines in both K and L groups. Absorber tests therefore distinguished groups without resolving every line.^[ref]

Henry Gwyn Jeffreys Moseley subsequently related the frequencies of corresponding spectral lines to atomic number. The approximate relation $\sqrt{\nu }=a(Z-b)$, with series-dependent constants $a,b$, is Moseley's law; its discovery should be distinguished from Barkla's identification of characteristic secondary radiation.^[ref]

A continuous incident frequency spectrum can contribute a continuous scattered background alongside discrete Characteristic X-rays. Here “scattered” identifies a production process, not a universal spectral shape: scattering of a narrow incident line need not make a continuum. In particular, the characteristic component is photon emission after vacancy creation, rather than simply the primary beam redirected. Source hardness, target substitution and absorber thickness probe different parts of that distinction. A surviving signal alone establishes neither an additional electron shell nor a fully resolved spectral line.

BCS theory describes a superconducting instability caused by attractive interactions between opposite-momentum fermions near a Fermi surface.

John Bardeen, Leon Neil Cooper and John Robert Schrieffer developed BCS theory in 1957, using attraction mediated by phonons.^[ref]

Weak-coupling Cooper pairs overlap. The Cooper instability reorganizes an unpaired Fermi surface; it is not Bose-Einstein condensation of compact, pre-existing molecules. The original paper explicitly distinguishes these pictures.^[ref]

Two complementary clues made the microscopic problem concrete. The superconducting isotope effect connected the transition to phonons.^[ref]

A 1957 transmission experiment used thin lead and tin films as samples in far-infrared and millimeter-microwave measurements. The measured transmission was converted to complex electrical conductivity, normalized to the normal-state value. Comparing film thickness, resistance, annealing and the two metals tested the response's reproducibility. Weak low-photon-energy absorption followed by an onset supported a superconducting energy gap; its extraction required a thin-film electrodynamic model.^[ref]

The later Giaever superconducting tunnelling experiment provided another way to resolve the superconducting energy gap through quantum tunnelling.^[ref] The derivations below explain what the model predicts, including the distinction between a single quasiparticle's minimum energy and the threshold for making two of them.

The diamond-cubic form of tin favoured below about $13{}^{\circ }\mathrm{C}$ at ambient pressure. Its lower density than white tin contributes to the damage associated with tin pest.

Indium oxide usually denotes indium(III) oxide, $\mathrm{I}{\mathrm{n}}_2{\mathrm{O}}_3$, a solid chemical compound of indium and oxygen. Formal oxidation states of $+3$ for indium and $-2$ for oxygen give charge balance: $2(3)+3(-2)=0$. The formula expresses the elemental ratio; it does not imply discrete molecules in the solid.^[ref]

Doping this oxide with tin produces the material family indium tin oxide, used for transparent conducting layers. Electrical and optical performance depend on charge-carrier density and preparation, so knowing the host compound's formula alone does not specify a film's conductivity.^[ref]

Indium tin oxide is a conducting oxide material based on indium oxide doped with tin. It is valued for combining substantial electrical conductivity with transmission of visible light, allowing a thin layer to function as an electrode through which light can pass. Its composition is not represented by one universal stoichiometric formula.^[ref]

The two properties probe different responses. Direct-current conduction measures mobile charge carriers, while optical transmission depends on frequency-dependent absorption and reflection as well as film thickness. Increasing carrier density can therefore change the optical response together with conductivity. Measurements of Hall effect and optical resonances help connect the electrical and optical descriptions of the same film.^[ref]

${\mathrm{S}}_4^{2+}$ is approximately square planar; $\mathrm{S}{\mathrm{n}}_5^{2-}$ is a closo trigonal bipyramid. Both have 22 valence electrons, $4(6)-2=22$ and $5(4)+2=22$, but their different local orbital requirements prevent inferring identical shapes from this total alone.

For the sulfur ring, four S–S sigma bonds use eight electrons and four in-plane lone pairs use another eight, leaving six electrons in the perpendicular cyclic pi system. The resulting filled bonding and degenerate nonbonding pi levels give a six-pi-electron aromatic description of a four-membered ring, consistent with equivalent S–S links in the ideal square. The out-of-plane p orbitals are retained; this is not a tetrahedral four-vertex closo cage.

For tin, allocate one mainly s-rich lone pair to each atom. The remaining $22-5(2)=12$ electrons form six skeletal pairs, exactly $n+1$ for $n=5$. Wade's rules therefore predict a trigonal bipyramid, with three equatorial vertices and two axial vertices. The axial pair is not joined by a polyhedral edge; its bonding is part of the delocalized three-dimensional framework. The contrast is a planar aromatic sigma/pi ring versus a three-dimensional multicentre-bonded Zintl cluster, rather than cationic charge alone imposing planarity or anionic charge alone imposing a polyhedron.

(Bi) and $(\beta \mathrm{Sn})$ are Bi-rich and Sn-rich terminal solid solutions, not intermetallic compounds. At the eutectic composition, cooling through $138{}^{\circ }\mathrm{C}$ givesThe two solids grow together as a fine eutectic microstructure, commonly lamellar or rod-like. Below about $13{}^{\circ }\mathrm{C}$, the tin-rich component has an equilibrium tendency to transform from metallic tetragonal white tin to diamond-cubic grey tin, with a substantial volume increase. This is tin pest, which can disrupt the microstructure mechanically. The dashed transition does not transform the Bi-rich phase into tin. Actual transformation can be slow and depend strongly on impurities and nucleation; crossing the line does not guarantee immediate disintegration.

Iron in nonoxidizing hydrochloric acid principally gives an iron(II) solution; tin in oxidizing aqua regia principally gives a tin(IV) solution. These are the two preparations paired most directly by “respectively”. Their contrast is clearer when the other acid treatment of each metal is considered as well. “Nitrohydrochloric acid” is the historical name for aqua regia, containing nitric and hydrochloric acids.

For iron in dilute hydrochloric acid,The fresh solution is typically pale green when sufficiently concentrated. Hydroxide gives a pale green precipitate of iron(II) hydroxide, which darkens and turns brown on exposure to air as oxidation proceeds. Ammonia can similarly precipitate a ferrous hydroxide rather than forming a stable soluble excess-ammonia complex under the usual test conditions. Ferricyanide gives a deep blue product; the modern structural account of this blue material should not be replaced by an overly literal formula inferred solely from the reagent names. Ferrous solution also reduces a suitable oxidant such as acidic permanganate:

If instead oxidizing acid treatment produces iron(III), the solution exhibits ferric reactions: hydroxide or Ammonia gives red-brown iron(III) hydroxide; thiocyanate gives a strong red colour; and ferrocyanide gives Prussian blue. Chloride complex formation affects colour and some equilibria, so “yellow” is not a universal iron(III) identity test. Oxidizing aqua regia supplies this ferric comparison rather than merely generating more of the same ferrous salt.

Tin in ordinary hydrochloric acid gives a tin(II) solution with hydrogen evolution:Its characteristic property is reducing power. With mercury(II) chloride, controlled addition can first form white mercury(I) chloride and then, with further reductant, grey metallic Mercury:The chloride formulae are useful net bookkeeping, not a complete statement of all aqueous chloro-complexes.

In aqua regia, tin is oxidized predominantly to tin(IV). A representative balance, choosing nitrogen monoxide as the nitrate-reduction product, isActual gas products depend on the acid conditions. Sufficient chloride and acidity retain tin in solution; dilution can cause hydrolysis and precipitation of hydrated tin(IV) oxide. This differs from the simple expectation that every dilution leaves unchanged molecular ${\mathrm{SnCl}}_4$ in water. Hydrogen sulfide in suitable acidic conditions gives yellow tin(IV) sulfide, compared with brown tin(II) sulfide from a stannous solution. Tin(IV) does not reproduce the characteristic reducing reaction of fresh tin(II) with mercuric chloride; reduction to tin(II) is needed first. Oxidation during storage can therefore change the reactions of a nominally stannous preparation.

In a suitably dilute, nonoxidizing chemical acid, hydrogen sulfide precipitates the sufficiently insoluble sulfides, including those of copper, lead, Mercury, bismuth, cadmium, arsenic, antimony and tin. “Sulphuretted hydrogen” is the historical name for hydrogen sulfide, ${\mathrm{H}}_2\mathrm{S}$. Oxidation state and acidity must be specified: the statement is not independent of every possible chemical solution condition.

Arsenic is now classed as a metalloid; the historical analytical grouping was not a rigorous modern division into metals and nonmetals. Dissolved silver also gives black ${\mathrm{Ag}}_2\mathrm{S}$ in acidic conditions. It is often absent from the conventional second analytical group because a preceding hydrochloric acid treatment has already removed it as silver chloride. Suitable gold and platinum solutions can likewise yield dark sulfide precipitates, although their speciation and reduction chemistry make a simple universal colour rule inappropriate. Thus an analytical group is a separation convention, not a list of every ion that can possibly react.

For a divalent metal ion, a useful net balance isThe selectivity follows from two coupled chemical equilibrium conditions. Hydrogen sulfide is a weak acid; increasing $[{\mathrm{H}}^{+}]$ suppresses its ionization. Approximately,Even this small sulfide activity can exceed the solubility product of very insoluble sulfides. More soluble sulfides, such as those of zinc and manganese, generally require less acidic or alkaline conditions. Consequently an excessively strong chemical acid, complex formation or an oxidizing medium can change the result. Colours alone are preliminary indications, not final identification.^[ref]

The traditional preparation treats iron(II) sulfide with a dilute nonoxidizing chemical acid:A gas-generating flask with controlled acid entry and a delivery outlet conducts the product to the test solution. The apparatus must permit gas flow and contain the effluent rather than accumulating pressure in a sealed vessel. Sulfuric acid in dilute form can replace hydrochloric acid; concentrated oxidizing acids are unsuitable for this simple preparation. Hydrogen sulfide is acutely toxic, and loss of odour perception makes smell an unreliable warning: the historical apparatus describes a laboratory principle, not a household test.^[ref]

Tin is the chemical element with atomic number 50 and symbol $\mathrm{Sn}$. It is a metal. Both $+2$ and $+4$ oxidation states are common. Its different solid allotropes have different structures, and tin-containing solders illustrate how alloy composition can change melting and mechanical properties.^[ref]

The +2 oxidation state of tin. The actual aqueous species can depend on pH, hydrolysis and ligands; a bare ionic formula is an analytical shorthand.

The +4 oxidation state of tin. The actual aqueous species can depend on pH, hydrolysis and ligands; a bare ionic formula is an analytical shorthand.

Walther Meissner and Robert Ochsenfeld found that cooling a sample into its superconducting state changes the surrounding magnetic field even when the applied field is held fixed. Their tin and lead experiments used a rotating search coil and a galvanometer to compare magnetic flux above and below the transition. The Meissner effect therefore requires more than zero electrical resistance: a superconductor has a distinctive magnetic response. Their hollow-tube measurements also showed why field in a cavity must be distinguished from field inside the superconducting material.^[ref]

The metallic tetragonal form of tin stable near ordinary room temperature at ambient pressure.