Assertion: bcc and ccp have same packing efficiency
Reason: Both have same number of atoms per unit cell and same arrangement

Options

A. If both assertion and reason are correct and reason is correct explanation for assertion
B. If both assertion and reason are correct but reason is not correct explanation for assertion
C. If assertion is correct but reason is incorrect
D. If both assertion and reason are incorrect

Explanation

To solve the question, we need to analyze the assertion and the reason provided regarding the body-centered cubic (BCC) and cubic close-packed (CCP) structures.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that BCC and CCP have the same packing efficiency.
- Packing efficiency is defined as the fraction of volume in a crystal structure that is occupied by the constituent particles (atoms).

2. **Calculating Packing Efficiency for BCC**:
- In a BCC unit cell, there are 2 atoms per unit cell (Z = 2).
- The packing efficiency for BCC can be calculated using the formula:
\[ \text{Packing Efficiency} = \frac{Z \times \text{Volume of one atom}}{\text{Volume of unit cell}} \]
- The packing efficiency for BCC is approximately 68%.

3. **Calculating Packing Efficiency for CCP**:
- In a CCP unit cell, there are 4 atoms per unit cell (Z = 4).
- Using the same formula for packing efficiency:
\[ \text{Packing Efficiency} = \frac{Z \times \text{Volume of one atom}}{\text{Volume of unit cell}} \]
- The packing efficiency for CCP is approximately 74%.

4. **Conclusion on the Assertion**:
- Since the packing efficiencies of BCC (68%) and CCP (74%) are different, the assertion that BCC and CCP have the same packing efficiency is **incorrect**.

5. **Understanding the Reason**:
- The reason states that both BCC and CCP have the same number of atoms per unit cell and the same arrangement.
- We already established that BCC has 2 atoms per unit cell and CCP has 4 atoms per unit cell.

6. **Conclusion on the Reason**:
- Since the number of atoms per unit cell is different (2 for BCC and 4 for CCP), the reason is also **incorrect**.

7. **Final Conclusion**:
- Both the assertion and the reason are incorrect. Therefore, the correct answer is that both the assertion and the reason are incorrect.

### Final Answer:
The correct answer is that both the assertion and the reason are incorrect.

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