Question

The number of atoms per unit cell in simple cubic, face-centered cubic, and body-centered cubic are:

• A. 1, 4, 2
• B. 4, 1, 2
• C. 2, 4, 1
• D. 4, 8, 2

Hint:

The number of atoms in a unit cell depends on how the atoms are arranged. Simple cubic has 1, face-centered cubic has 4, and body-centered cubic has 2 atoms per unit cell.

Answer 1

The Correct Option is A

Step 1: Simple Cubic Unit Cell. In a simple cubic unit cell, one atom is present at each corner. As each corner atom is shared by 8 unit cells, the total atoms per unit cell are calculated as: \[ \text{Atoms per unit cell} = \frac{1}{8} \times 8 = 1 \]

Step 2: Face-Centered Cubic (FCC) Unit Cell. A face-centered cubic unit cell contains atoms at the 8 corners (each shared by 8 unit cells) and 6 atoms at the centers of the faces (each shared by 2 unit cells). Consequently, the total atoms per unit cell are: \[ \text{Atoms per unit cell} = \frac{1}{8} \times 8 + \frac{1}{2} \times 6 = 4 \]

Step 3: Body-Centered Cubic (BCC) Unit Cell. A body-centered cubic unit cell has an atom at each corner (shared by 8 unit cells) and one atom at the center (not shared). The total atoms per unit cell are: \[ \text{Atoms per unit cell} = \frac{1}{8} \times 8 + 1 = 2 \]

Step 4: Conclusion. Therefore, the number of atoms per unit cell for simple cubic, face-centered cubic, and body-centered cubic unit cells are 1, 4, and 2, respectively. Option (1) is the correct answer.