Which one of the following schemes of ordering closed packed sheets of equal sized spheres do not generate close packed lattice?

Options

A. ABCABC
B. ABACABAC
C. ABBAABBA
D. ABCBCABCBC

Answer

To determine which scheme of ordering closed-packed sheets of equal-sized spheres does not generate a close-packed lattice, we will analyze each option systematically.

### Step-by-Step Solution:

1. **Understanding Close-Packed Structures:**
- Close-packed structures are arrangements of spheres that maximize the packing efficiency. The most common types are Face-Centered Cubic (FCC) and Hexagonal Close Packing (HCP).
- In these structures, the arrangement of layers typically alternates in a specific sequence to maintain the close-packed nature.

2. **Analyzing Each Option:**
- **Option 1: A, B, C, A, B, C**
- This option alternates layers in a repeating sequence. It follows the pattern of close packing and can generate a close-packed lattice.

- **Option 2: A, B, A, C, A, B, A, C**
- This option also maintains a sequence that allows for close packing, as it does not repeat the same layer consecutively.

- **Option 3: A, B, B, A, A, B, B**
- In this option, the layers B and A repeat consecutively (B, B and A, A). This violates the principle of close packing as it has two consecutive layers that are identical. Therefore, it does not generate a close-packed lattice.

- **Option 4: A, B, C, B, C, A**
- This option has a distinct arrangement where no two consecutive layers are the same, allowing for a close-packed structure.

3. **Conclusion:**
- Based on the analysis, **Option 3 (A, B, B, A, A, B, B)** is the arrangement that does not generate a close-packed lattice due to the repetition of layers.

### Final Answer:
**Option 3: A, B, B, A, A, B, B** does not generate a close-packed lattice.