/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 69 Ca metal forms a face-centered c... [FREE SOLUTION] | 91Ó°ÊÓ

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Ca metal forms a face-centered cubic closest-packed unit cell. Roughly sketch this unit cell.

Short Answer

Expert verified
Draw a cube with atoms at each corner and the center of each face.

Step by step solution

01

Understanding a Face-Centered Cubic (FCC) Unit Cell

A face-centered cubic (FCC) unit cell is a type of cubic lattice structure where atom centers are located at each of the corners and at the centers of all the faces of the cube. This means there are atoms at the 8 corners of the cube and one additional atom at the center of each of the 6 cube faces.
02

Determine the Number of Atoms in the Unit Cell

In an FCC unit cell, each corner atom is shared by 8 neighboring cubes, contributing 1/8th of an atom per corner to the unit cell. Each face-centered atom is shared by 2 cubes, contributing 1/2 of an atom per face to the unit cell. Therefore, the total number of atoms within a single FCC unit cell can be calculated as follows: - Corner atoms: 8 corners x 1/8 per corner = 1 atom - Face-centered atoms: 6 faces x 1/2 per face = 3 atoms Total: 1 + 3 = 4 atoms per unit cell.
03

Sketch the FCC Unit Cell

To roughly sketch the FCC unit cell, draw a cube to represent the basic repeat structure of the crystal. Mark an atom at each of the 8 corners and at the center of each of the 6 faces. These face-centered atoms complete the arrangement, giving the structure its name. Remember to sketch lightly and label the face-centered, and corner atoms for clarity

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Crystal Lattice
A crystal lattice is a three-dimensional arrangement of atoms or molecules in a distinct pattern that defines the structure of a crystal. Think of it as the invisible framework that holds all the crystal's building blocks together in a repeatable pattern. This organizational system not only determines the crystal's outer shape but also influences its physical properties.
In the case of metals, a common lattice arrangement is the face-centered cubic (FCC) structure. Metal atoms are small and efficient packers, so they tend to arrange themselves in ways that fill space most efficiently. The FCC arrangement is one of the ways they achieve this.
The FCC structure is considered dense because the atoms are packed closely together. It features atoms located at each of the cube's eight corners and additional atoms situated at the centers of each of the cube's six faces. This setup maximizes the contact between atoms, resulting in a sturdy, stable configuration.
Calcium Metal Structure
Calcium metal is a typical example of a metal that forms a face-centered cubic lattice structure. This structure is not unique to calcium; many metals such as aluminum, copper, and lead also adopt this form because of its packing efficiency.
In the FCC unit cell that calcium atoms form, every atom is surrounded by and in contact with 12 other atoms. This kind of tight atomic packing is called 'closest packing', which helps optimize the overall stability and strength of the metal.
This close packing in calcium, specifically, makes it flexible and allows it to conduct electricity effectively. These are important traits for its various industrial uses, including metallurgy and electronics. By understanding the atomic arrangement within calcium's FCC structure, scientists and engineers can better predict and manipulate the metal's properties.
Atomic Arrangement
The atomic arrangement within a face-centered cubic unit cell is highly ordered and symmetrical. This orderly arrangement is a key aspect of why certain metals exhibit the properties they do.
In the FCC structure, you have atoms at the eight corners of the cube, with each corner atom being shared among eight neighboring unit cells. Thus, each corner atom contributes only 1/8 of an atom to the individual unit cell it resides in.
Additionally, there are face-centered atoms, one on each of the six faces of the cube. These atoms are shared by just two cells, thereby contributing 1/2 of an atom to each unit cell. When you add them all up, an FCC unit cell contains a total of 4 atoms (1 from corners + 3 from faces). This precise arrangement contributes to the uniformity and strength of the metal, as well as its high density.

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Most popular questions from this chapter

Name all of the species in the following reaction. $$ \begin{array}{l} 4 \mathrm{NaCl}(s)+2 \mathrm{H}_{2} \mathrm{SO}_{4}(a q)+\mathrm{MnO}_{2}(s) \\\ \quad \longrightarrow 2 \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)+\mathrm{MnCl}_{2}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Cl}_{2}(g) \end{array} $$ Is the reaction an oxidation-reduction reaction? If so, what is oxidized and what is reduced?

Xe forms a limited number of compounds. Calculate the oxidation number of the xenon atom in the following compounds or ions and describe any trends in the oxidation states. (a) \(\mathrm{XeF}_{2}\) (b) \(\mathrm{XeF}_{4}\) (c) \(\mathrm{XeOF}_{2}\) (d) \(\mathrm{XeF}_{6}\) (e) \(\mathrm{XeOF}_{4}\) (f) \(\mathrm{XeO}_{3}\) (g) \(\mathrm{XeO}_{4}\) (h) \(\mathrm{XeO}_{6}^{4-}\)

Write the formulas for the following compounds. (a) beryllium fluoride (b) magnesium nitride (c) calcium carbide (d) barium peroxide (e) potassium carbonate

The differences among the electronegativities of the atoms in the compounds \(\mathrm{SeO}_{2}, \mathrm{CaH}_{2},\) and \(\mathrm{Cs}_{3} \mathrm{Sb}\) are all about the same. Yet only one of these compounds conducts electricity in the solid state, only one has a high melting point and dissolves in water to give a solution that conducts electricity, and only one has a relatively low melting point. Identify each of the compounds and explain your identification.

Which of the following elements forms bonds with fluorine that are the most covalent? (a) \(\mathrm{P}\) (b) \(\mathrm{Ca}\) (c) \(\mathrm{Al}\) (d) \(\mathrm{O}\) (e) Se

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