Question

In the closest packing of atoms, there are: (a) one tetrahedral void and two octahedral voids per atom (b) two tetrahedral voids and one octahedral void per atom (c) two of each tetrahedral and octahedral voids per atom (d) one of each tetrahedral and octahedral void per atom

Short answer

There are two tetrahedral voids and one octahedral void per atom in the closest packing of atoms, so the correct option is (b).

Step-by-step solution

Understand Concepts of Voids in Close Packing

In a close-packed structure of atoms, there are spaces between the atoms where other, typically smaller, atoms can fit. These spaces are called voids and they come in two main types: tetrahedral and octahedral. A tetrahedral void is formed when three atoms in one layer are covered by one atom in the adjacent layer forming a tetrahedron. An octahedral void is surrounded by six atoms, forming an octahedron.

Determine the Number of Tetrahedral Voids per Atom

For every atom in a close-packed structure, there are two tetrahedral voids. This is because each atom in the structure is a part of two tetrahedral voids.

Determine the Number of Octahedral Voids per Atom

The number of octahedral voids per atom in a close-packed structure is equal to the number of atoms. This means there is one octahedral void for each atom.

Identify the Correct Option

Since there are two tetrahedral voids and one octahedral void associated with each atom in a close-packed structure, the correct option is (b) two tetrahedral voids and one octahedral void per atom.

Key concepts

Tetrahedral Void

Imagine placing marbles in a triangular manner — they create a shape similar to a three-legged stool. Now, if we gently nestle another marble on top of these three, we've created a tetrahedral void in the space where the four marbles touch. In crystallography, a tetrahedral void is a small, empty space amidst four atoms when they are packed in a crystal lattice.

Each tetrahedral void is shaped like a pyramid with a triangular base, hence the name 'tetrahedral'. This tiny pocket is not vast enough to house another atom of the same size, but it can accommodate smaller atoms or ions.

Why does this matter? In materials like alloys and ceramics, these voids could be the reason for important properties such as electrical conductivity and structural stability. In our close packing exercise, for every atom, there are exactly two tetrahedral voids. These voids are what makes the structure of materials so wonderfully intricate and useful.

Octahedral Void

Let’s turn from pyramids to diamonds — or at least the diamond-shape of the octahedral void, a gap surrounded by six atoms in a crystal lattice. Picture a layer of atoms lying flat and a second layer nestling into the gaps of the first. The space that’s formed in between the first and second layer, but also touching the atoms of a coming third layer, is our octahedral void.

Six atoms, forming an eight-faced solid known as an octahedron, surround each void. In the close-packing puzzle, these are crucial because they show up at a one-to-one ratio with the atoms. This means if you have a close-packed structure with, say, 100 atoms, you will also find 100 octahedral voids beckoning for potential smaller atoms.

If we relate this to our exercise problem, these octahedral voids are critical for understanding the way different atoms can potentially interact within a material. With this, we earn a clearer image of its possible physical and chemical characteristics.

Crystal Structure

Dive into a crystal, and what do you find? Regular patterns and pathways, a microscopic maze of atoms or molecules arranged in an orderly fashion. This arrangement is described as a crystal structure, and it's like the framework of a building at the atomic level.

Every crystal structurally consists of a unit cell, a repeating entity, akin to the bricks in a wall, that contains the geometric and positional information of every constituent particle in the crystal.

While our exercise specifically involves packing atoms closely, in real life it is not just atoms, but ions and molecules that come together to form various crystal structures, everything from the ice in your freezer to the salt on your table. The arrangement, size, and type of the voids (tetrahedral or octahedral) affect the crystal structure, ultimately influencing the material's properties such as melting point, density, and how it reacts to stress.

Close-Packed Structure

Close that book, pack those atoms tightly, and you have a close-packed structure. In such structures, atoms are arranged in a way that they take up the maximum possible space, like stacked spheres — think of oranges in a box or balls in a pit at a playground.

There are several types of close-packed structures, with the most common being face-centered cubic (FCC) and hexagonal close-packed (HCP). Both structures maximize space usage, minimizing voids.

In relevance to our exercise, understanding the close-packed structure is valuable because it affects how many tetrahedral and octahedral voids exist. In essence, for every single atom in a close-packed structure, there are two homes (tetrahedral voids) and at least one pit stop (octahedral void) for other, usually smaller, atoms. It's this clever interplay of space that determines the hidden potential a material might possess, from strength to conductivity to how it might interact with other materials.