What is the number of tetrahedral voids per atom in a crystal?

Options

A. 1
B. 2
C. 6
D. 8

Explanation

To determine the number of tetrahedral voids per atom in a crystal, we can follow these steps:

### Step 1: Understand the Concept of Tetrahedral Voids
In a crystal lattice, tetrahedral voids are the empty spaces that can accommodate smaller atoms or ions. These voids are formed when four atoms are arranged in a tetrahedral shape.

### Step 2: Identify the Relationship Between Tetrahedral Voids and Atoms
In a unit cell of a crystal, the number of tetrahedral voids is related to the number of atoms present. Specifically, for every atom in the unit cell, there are two tetrahedral voids.

### Step 3: Calculate the Number of Tetrahedral Voids
If we denote the number of atoms in the unit cell as \( n \), then the total number of tetrahedral voids in that unit cell is given by:
\[ \text{Total Tetrahedral Voids} = 2n \]

### Step 4: Determine the Number of Tetrahedral Voids Per Atom
To find the number of tetrahedral voids per atom, we divide the total number of tetrahedral voids by the total number of atoms:
\[ \text{Tetrahedral Voids per Atom} = \frac{\text{Total Tetrahedral Voids}}{\text{Total Number of Atoms}} = \frac{2n}{n} \]

### Step 5: Simplify the Expression
When we simplify the expression, we find:
\[ \text{Tetrahedral Voids per Atom} = 2 \]

### Final Answer
Thus, the number of tetrahedral voids per atom in a crystal is **2**.

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