Ionic radii of cation A+ and anion B– are 102 and 181 pm, respectively. These ions are allowed to crystallize into an ionic solid. This crystal has cubic close packing for B–. A+ is present in all octahedral voids. The edge length of the unit cell of the crystal AB is _____pm. (Nearest integer)
Correct Answer: 566
Solution and Explanation
In cubic close packing, octahedral voids form at edge centers and body center of the cube
a =\(2(r_A^+ + r_B^-)\)
a = 2 (102 + 181)
a = 566 pm
So, the answer is 566 pm.
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Concepts Used:
Crystal Lattices and Unit Cells
A crystal lattice is a repeating pattern of atoms, ions, or molecules in a solid. The lattice structure is formed due to the arrangement of the constituent particles, which can be visualized as a three-dimensional grid. The lattice structure of a crystal is determined by its unit cell, which is the smallest repeating unit of the crystal lattice.
A unit cell is a volume of space that contains one or more atoms or ions and is repeated throughout the crystal lattice. The shape and size of the unit cell determines the overall shape and size of the crystal lattice. There are several types of unit cells, including simple cubic, body-centered cubic, and face-centered cubic.
Read Also: Crystallization
In a simple cubic lattice, each lattice point is surrounded by six neighboring lattice points, forming a cube. In a body-centered cubic lattice, there is an additional atom at the center of the cube, while in a face-centered cubic lattice, there is an additional atom at each face of the cube.
The arrangement of atoms, ions, or molecules in a crystal lattice affects its physical and chemical properties, such as density, melting point, and optical properties. For example, the arrangement of carbon atoms in a diamond crystal lattice gives it its characteristic hardness and transparency.
Understanding the crystal lattice structure and unit cell of a material is important in materials science and engineering, as it can help to predict its properties and behavior under different conditions. Techniques such as X-ray crystallography can be used to determine the crystal lattice structure of materials.