Calculate the value of `(Z)/(10)`. Where
Z = co-ordination number of 2D-square close packing
+
Co-ordination number of 2D-hcp
+
Co-ordination number of 3D-square close packing
+
Co-ordination number of 3D, ABCABC........packing
+
Co-ordiantional number of 3D, ABAB.......packing .

Answer

To solve the problem, we need to calculate the value of \( \frac{Z}{10} \), where \( Z \) is the sum of the coordination numbers for various types of packing. Let's break it down step by step.

### Step 1: Identify the Coordination Numbers

1. **2D Square Close Packing**:
- In this arrangement, each atom touches 4 other atoms.
- **Coordination Number (CN)** = 4

2. **2D Hexagonal Close Packing (hcp)**:
- In this arrangement, each atom touches 6 other atoms.
- **Coordination Number (CN)** = 6

3. **3D Square Close Packing**:
- In this arrangement, each atom also touches 6 other atoms.
- **Coordination Number (CN)** = 6

4. **3D ABCABC Packing**:
- In this arrangement, each atom touches 12 other atoms (6 in its own layer, 3 in the layer above, and 3 in the layer below).
- **Coordination Number (CN)** = 12

5. **3D ABAB Packing**:
- Similar to the ABCABC packing, each atom touches 12 other atoms (6 in its own layer, 3 in the layer above, and 3 in the layer below).
- **Coordination Number (CN)** = 12

### Step 2: Calculate the Total Coordination Number \( Z \)

Now, we sum up all the coordination numbers:

\[ Z = 4 \, (\text{2D Square}) + 6 \, (\text{2D hcp}) + 6 \, (\text{3D Square}) + 12 \, (\text{3D ABCABC}) + 12 \, (\text{3D ABAB}) \]

Calculating this gives:

\[ Z = 4 + 6 + 6 + 12 + 12 = 40 \]

### Step 3: Calculate \( \frac{Z}{10} \)

Now, we need to find \( \frac{Z}{10} \):

\[ \frac{Z}{10} = \frac{40}{10} = 4 \]

### Final Answer

Thus, the value of \( \frac{Z}{10} \) is **4**.

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