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Cerium is a lanthanide chemical element with symbol $\mathrm{Ce}$ and atomic number $58$. Its accessible $+3$ and $+4$ oxidation states distinguish much of its chemistry from rare earths dominated by only $+3$.^[ref]

Changing the cerium oxidation state exchanges an electron with the surroundings and can couple to oxygen defects in cerium-containing oxides. Such redox flexibility helps explain why composition, defect population and chemical environment must be specified when describing a cerium material.

Erbium is the chemical element with atomic number 68 and symbol $\mathrm{Er}$. It is a lanthanide. Erbium ions in glass can absorb and emit infrared light near telecommunications wavelengths. Erbium-doped optical amplifiers exploit these electronic transitions, linking an element's energy levels to long-distance optical communication.^[ref]

Europium is the chemical element with atomic number 63 and symbol $\mathrm{Eu}$. It is a lanthanide. Its $+2$ state is unusually accessible compared with many neighboring lanthanides. Europium ions are used in luminescent materials, where changes in electronic energy are emitted as characteristic colors.^[ref]

Gadolinium is the chemical element with atomic number 64 and symbol $\mathrm{Gd}$. It is a lanthanide. The $\mathrm{G}{\mathrm{d}}^{3+}$ ion has seven unpaired 4f electrons, giving it strong paramagnetism. This connects atomic electron configuration with magnetic behavior and with the effect of coordinated gadolinium on nearby nuclear-spin relaxation.^[ref]

A lanthanide is an element in the series from lanthanum, atomic number 57, through lutetium, atomic number 71. The progression is associated with filling the 4f shell and the systematic size change called the lanthanide contraction.

Many lanthanides favour trivalent ions with similar coordination chemistry. Their similarity makes separation demanding, while differences in ionic size and accessible oxidation states permit selectivity.

Two bidentate bipyridine ligands provide four N donors and three terminal NCS ligands provide three more. Adding one water gives $n=1$ and coordination number eight:Eight-coordinate arrangements, distorted between familiar ideal polyhedra, are plausible for a sterically crowded Eu(III) centre. A second water would give coordination number nine, which is not forbidden for a lanthanide; the requested value is a chemically motivated prediction, not something fixed by charge balance. Diffraction or a direct hydration-number measurement is needed to establish it uniquely.

Not as a general aqueous separation reaction for the other lanthanides. Most strongly favour the trivalent state in ordinary water chemistry. Ce(IV) is unusually accessible because it has the empty $4f$ shell and is strongly stabilized by oxide formation. Some other lanthanides have accessible alternative oxidation states, such as Eu(II), and higher oxides of Pr or Tb can exist under suitable conditions; this does not imply that they undergo the same Ce(III)/Ce(IV) pH-controlled aqueous oxidation.

A natural feed can contain thorium and uranium, as well as other lanthanides. Th(IV) hydrolyses readily and can accompany the cerium precipitate; uranium speciation depends on its oxidation state and the ligands present. Raising pH too far also precipitates other rare-earth hydroxides. Even before their bulk precipitation thresholds, adsorption and coprecipitation on a high-area hydrated cerium oxide can contaminate the solid. Local high-pH zones during base addition and incomplete Ce(III) oxidation make the separation less reproducible.

Thus a cerium-rich precipitate need not be pure cerium. A sensible test measures the Ce oxidation state, analyses both filtrate and washed solid, and includes thorium-containing and thorium-free mixtures; otherwise low dissolved cerium could be mistaken for selective purification.

Use the balanced aqueous-acid reactionA Hess cycle first atomizes the metal, then ionizes its gas-phase atoms, then hydrates the triply charged gas ions:Close the reference leg by combining the three electrons with $3{\mathrm{H}}^{+}(\mathrm{aq})$ to make $\frac{3}{2}{\mathrm{H}}_2(\mathrm{g})$. Calling that element-independent contribution $C_H$ givesA single-ion standard enthalpy of formation uses the conventional hydrogen-ion reference; it must not be treated as a balanced creation of net charge from neutral metal without an electron/reference term. The constant hydrogen leg does not affect comparisons along the lanthanide series.

Samarium is the chemical element with atomic number 62 and symbol $\mathrm{Sm}$. It is a lanthanide. Samarium-cobalt alloys provide strong permanent magnets. It also has useful $+2$ and $+3$ chemistry, illustrating that the common trivalent pattern of the lanthanides has chemically important exceptions.^[ref]

Ytterbium is the chemical element with atomic number 70 and symbol $\mathrm{Yb}$. It is a lanthanide. It has important $+2$ and $+3$ chemistry. Its narrow optical transitions are useful in precision atomic experiments, showing how a chemical element can also provide a highly reproducible spectroscopic reference.^[ref]

Yttrium is the chemical element with atomic number 39 and symbol $\mathrm{Y}$. It is a metal. Its common oxidation state is $+3$, and its chemistry resembles that of many lanthanides. Yttrium-containing oxides are used in optical and ceramic materials, showing why a minor compositional change can alter a solid's properties.^[ref]