Textbook Question
The density of an unknown metal is 12.3 g/cm3, and its atomic radius is 0.134 nm. It has a face-centered cubic lattice. Find the atomic mass of this metal
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Ch.12 - Solids and Modern Material
Chapter 12, Problem 85
Potassium chloride crystallizes in the rock salt structure. Estimate the density of potassium chloride using the ionic radii provided in Chapter 8.
Verified step by step guidance1
Identify the type of crystal structure: Potassium chloride (KCl) crystallizes in the rock salt structure, which is a face-centered cubic (FCC) lattice.
Determine the formula unit mass of KCl: Use the atomic masses of potassium (K) and chlorine (Cl) from the periodic table to calculate the molar mass of KCl.
Calculate the volume of the unit cell: Use the ionic radii provided to estimate the edge length of the cubic unit cell. In the rock salt structure, the edge length (a) can be approximated as twice the sum of the radii of the cation and anion.
Determine the number of formula units per unit cell: In the rock salt structure, there are 4 formula units of KCl per unit cell.
Estimate the density: Use the formula for density, \( \text{density} = \frac{\text{mass of formula units in unit cell}}{\text{volume of unit cell}} \), to calculate the density of KCl.
Related Practice
Textbook Question
An unknown metal is found to have a density of 7.8748 g/cm3 and to crystallize in a body-centered cubic lattice. The edge of the unit cell is 0.28664 nm. Calculate the atomic mass of the metal.
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Open Question
When spheres of radius r are packed in a body-centered cubic arrangement, they occupy 68.0% of the available volume. Use the fraction of occupied volume to calculate the value of a, the length of the edge of the cube, in terms of r.
Textbook Question
Calculate the fraction of empty space in cubic closest packing to five significant figures.
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Open Question
What is a tetrahedral site in a closest-packed lattice formed by?
Textbook Question
X-ray diffractometers often use metals that have had their core electrons excited as a source of X-rays. Consider the 2p → 1s transition for copper, which is called the K⍺ transition. Calculate the wavelength of X-rays (in Å) given off by the K⍺ transition if the energy given off by a mole of copper atoms is 7.77⨉105 kJ.(1Å = 10-10 m)
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