In ABCABC packing of atoms, which of the following cubic lattice has 74% space occupied by the atoms?

Options

A. Body centred cubic lattice
B. Simple cubic lattic
C. Hexagonal closed lattice
D. Cubic closed lattice

Explanation

To solve the question regarding which cubic lattice has a 74% space occupied by atoms in ABCABC packing, we can follow these steps:

### Step 1: Understand Packing Fraction
The packing fraction is defined as the volume of the atoms in a unit cell divided by the volume of the unit cell itself. It is expressed as a percentage.

### Step 2: Identify Different Types of Cubic Lattices
There are several types of cubic lattices, including:
- Simple Cubic (SC)
- Body-Centered Cubic (BCC)
- Face-Centered Cubic (FCC)

### Step 3: Calculate Packing Fractions for Each Lattice
1. **Body-Centered Cubic (BCC)**: The packing fraction is approximately 68%.
2. **Simple Cubic (SC)**: The packing fraction is approximately 52.4%.
3. **Face-Centered Cubic (FCC)**: The packing fraction is 74%.

### Step 4: Analyze the Packing Types
- The question specifies ABCABC packing, which refers to the face-centered cubic (FCC) arrangement. This is because FCC has a close packing structure that follows the ABCABC sequence.

### Step 5: Conclusion
Since the face-centered cubic lattice has a packing fraction of 74%, and it corresponds to the ABCABC packing arrangement, the answer to the question is:

**Answer: Face-Centered Cubic (FCC) lattice has 74% space occupied by the atoms.**

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