Question

In Cubic lattice,

(A) For face centered cubic (fcc) lattice, effective number of atoms per unit cell is 2
(B) For body centered cubic (bcc) lattice, effective number of atoms per unit cell is 4
(C) \(a = b = c\), and \(\alpha = \beta = \gamma = 90^\circ\), where \(a\), \(b\), \(c\) are edge lengths and \(\alpha\), \(\beta\), \(\gamma\) are axial angles
(D) For simple cubic (sc) lattice, effective number of atoms per unit cell is 1
Choose the correct answer from the options given below:

• A. (A), (B) and (D) only.
• B. (A), (B) and (C) only.
• C. (C) and (D) only.
• D. (B), (C) and (D) only.

Hint:

FCC has 4 atoms per unit cell, BCC has 2, and SC has 1. All cubic unit cells have \(a = b = c\) and \(\alpha = \beta = \gamma = 90^\circ\).

Answer 1

The Correct Option is A

Step 1: Face-Centered Cubic (FCC).
- In FCC, atoms are located at the corners and centers of the faces of the unit cell.
- The effective number of atoms per unit cell is 4 (not 2).
Step 2: Body-Centered Cubic (BCC).
- In BCC, there is one atom at each corner and one at the center of the unit cell.
- The effective number of atoms per unit cell is 2, not 4.
Step 3: Simple Cubic (SC).
- In SC, there is one atom at each corner of the unit cell.
- The effective number of atoms per unit cell is 1.
Step 4: Conclusion. Thus, the correct answers are: \[ \text{(A), (B), (D) only} \]
Final Answer: \[ \boxed{\text{(A), (B) and (D) only}} \]