Question

The correct statements about SC lattice are:
A. The number of atoms per unit cell is 1
B. Its packing factor is 0.52
C. Iron is an example of SC lattice
D. Its Coordination Number is 6
Choose the correct answer from the options given below:

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

Hint:

It is crucial to memorize the key properties (number of atoms, coordination number, packing factor, and relationship between 'a' and 'r') for the three main cubic lattices: Simple Cubic (SC), Body-Centered Cubic (BCC), and Face-Centered Cubic (FCC). These are very frequently tested.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This question tests the fundamental properties of the Simple Cubic (SC) crystal lattice structure. We need to evaluate the correctness of each given statement.
Step 2: Detailed Explanation:
A. The number of atoms per unit cell is 1: In an SC lattice, there is one atom at each of the 8 corners of the cube. Each corner atom is shared by 8 unit cells. Therefore, the effective number of atoms per unit cell is \( 8 \times \frac{1}{8} = 1 \). This statement is correct.
B. Its packing factor is 0.52: The Atomic Packing Factor (APF) is the fraction of volume in a crystal structure that is occupied by atoms. For an SC lattice, \( \text{APF} = \frac{\text{Volume of atoms}}{\text{Volume of unit cell}} = \frac{1 \times \frac{4}{3}\pi r^3}{a^3} \). In an SC lattice, \( a = 2r \). So, \( \text{APF} = \frac{\frac{4}{3}\pi r^3}{(2r)^3} = \frac{\frac{4}{3}\pi r^3}{8r^3} = \frac{\pi}{6} \approx 0.5236 \). This statement is correct.
C. Iron is an example of SC lattice: This statement is incorrect. Iron (Fe) crystallizes in a Body-Centered Cubic (BCC) structure at room temperature (alpha-iron) and a Face-Centered Cubic (FCC) structure at higher temperatures (gamma-iron). The only element known to have a simple cubic structure under standard conditions is Polonium (Po).
D. Its Coordination Number is 6: The coordination number is the number of nearest neighbors for a given atom. In an SC lattice, each atom has one nearest neighbor along the positive and negative direction of each of the three axes (x, y, z), for a total of 6 nearest neighbors. This statement is correct.
Step 3: Final Answer:
Statements A, B, and D are correct, while statement C is incorrect. Therefore, the correct option includes A, B, and D only.