Ch.12 - Solids and Solid-State Materials

Problem 139

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Chapter 12, Problem 139

Europium(II) oxide is a semiconductor with a band gap of 108 kJ/mol. Below 69 K, it is also ferromagnetic, meaning all the unpaired electrons on europium are aligned in the same direction. How many f electrons are present on each europium ion in EuO? (In lanthanide ions the 4f orbitals are lower in energy than the 6s orbitals.)

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<insert step 1> Determine the electron configuration of a neutral europium (Eu) atom. Europium is a lanthanide with an atomic number of 63, so its electron configuration is [Xe] 4f^7 6s^2.>

<insert step 2> Identify the oxidation state of europium in EuO. In EuO, europium is in the +2 oxidation state, meaning it has lost two electrons.>

<insert step 3> Determine which electrons are lost when europium forms a +2 ion. Since the 4f orbitals are lower in energy than the 6s orbitals, the electrons are removed from the 6s orbital first.>

<insert step 4> Calculate the number of f electrons remaining on the europium ion. After losing the two 6s electrons, the europium ion retains its 4f^7 configuration.>

<insert step 5> Conclude that there are 7 f electrons present on each europium ion in EuO.>

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electron Configuration

Electron configuration describes the distribution of electrons in an atom's orbitals. For europium (Eu), which has an atomic number of 63, the electron configuration is [Xe] 4f^7 6s^2. This indicates that europium has seven electrons in the 4f subshell and two in the 6s subshell, which is crucial for understanding its chemical properties and behavior in compounds like europium(II) oxide.

Lanthanide Contraction

Lanthanide contraction refers to the gradual decrease in the size of the lanthanide ions as the atomic number increases. This occurs due to the increasing nuclear charge that is not fully offset by the shielding effect of the 4f electrons. Understanding this concept is essential for predicting the properties of europium ions, including their electron configurations and how they interact in compounds.

Ferromagnetism

Ferromagnetism is a phenomenon where certain materials exhibit spontaneous magnetization due to the alignment of unpaired electron spins. In the case of europium(II) oxide, below 69 K, the unpaired 4f electrons align in the same direction, resulting in ferromagnetic properties. This concept is important for understanding the magnetic behavior of materials and their applications in technology.

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Textbook Question

A cube-shaped crystal of an alkali metal, 1.62 mm on an edge, was vaporized in a 500.0 mL evacuated flask. The resulting vapor pressure was 12.5 mm Hg at 802 °C. The structure of the solid metal is known to be body-centered cubic. (b) Use the data in Figure 5.19 to identify the alkali metal.

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Textbook Question

A cube-shaped crystal of an alkali metal, 1.62 mm on an edge, was vaporized in a 500.0 mL evacuated flask. The resulting vapor pressure was 12.5 mm Hg at 802 °C. The structure of the solid metal is known to be body-centered cubic. (c) What are the densities of the solid and the vapor in g>cm3?

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Textbook Question

Assume that 1.588 g of an alkali metal undergoes complete reaction with the amount of gaseous halogen contained in a 0.500 L flask at 298 K and 755 mm Hg pressure. In the reaction, 22.83 kJ is released 1ΔH = -22.83 kJ2. The product, a binary ionic compound, crystallizes in a unit cell with anions in a face-centered cubic arrangement and with cations centered along each edge between anions. In addition, there is a cation in the center of the cube. (c) Sketch a space-filling, head-on view of the unit cell, labeling the ions. Are the anions in contact with one another?

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Textbook Question

The mineral wustite is a nonstoichiometric iron oxide with the empirical formula FexO, where x is a number slightly less than 1. Wustite can be regarded as an FeO in which some of the Fe sites are vacant. It has a density of 5.75 g>cm3, a cubic unit cell with an edge length of 431 pm, and a facecentered cubic arrangement of oxygen atoms. (c) Each Fe atom in wustite is in either the +2 or the +3 oxidation state. What percent of the Fe atoms are in the +3 oxidation state?

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Textbook Question

The mineral wustite is a nonstoichiometric iron oxide with the empirical formula FexO, where x is a number slightly less than 1. Wustite can be regarded as an FeO in which some of the Fe sites are vacant. It has a density of 5.75 g>cm3, a cubic unit cell with an edge length of 431 pm, and a facecentered cubic arrangement of oxygen atoms. (d) Using X rays with a wavelength of 70.93 pm, at what angle would third-order diffraction be observed from the planes of atoms that coincide with the faces of the unit cells? Third-order diffraction means that the value of n in the Bragg equation is equal to 3.

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Textbook Question

The alkali metal fulleride superconductors M3C60 have a cubic closest-packed (face-centered cubic) arrangement of nearly spherical C60 3- anions with M+ cations in the holes between the larger C603- ions. The holes are of two types: octahedral holes, which are surrounded octahedrally by six C603- ions; and tetrahedral holes, which are surrounded tetrahedrally by four C603- ions. (c) Specify fractional coordinates for all the octahedral and tetrahedral holes. (Fractional coordinates are fractions of the unit cell edge lengths. For example, a hole at the center of the cell has fractional coordinates 12, 12, 12.)

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