Question

What is the total number of atoms in BCC crystal lattice having \( 1.8 \times 10^{20} \) unit cells?

• A. \( 9.0 \times 10^{20} \)
• B. \( 1.8 \times 10^{20} \)
• C. \( 3.6 \times 10^{20} \)
• D. \( 7.2 \times 10^{20} \)

Hint:

Remember: BCC has 2 atoms per unit cell, FCC has 4, and simple cubic has 1. Always multiply by the number of unit cells.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We have a body-centered cubic (BCC) crystal lattice with a given number of unit cells: \( 1.8 \times 10^{20} \). We need the total number of atoms present.

Step 2: Key Formula or Approach:
In a BCC unit cell, there is 1 atom at the center and 8 atoms at the corners. Each corner atom is shared by 8 unit cells, so contribution from corners = \( 8 \times \frac{1}{8} = 1 \) atom. The center atom belongs entirely to one unit cell. Total atoms per BCC unit cell = \( 1 + 1 = 2 \).

Step 3: Detailed Explanation:
Number of atoms = (number of unit cells) \(\times\) (atoms per unit cell).
\( \text{Total atoms} = (1.8 \times 10^{20}) \times 2 = 3.6 \times 10^{20} \).

Step 4: Final Answer:
The total number of atoms is \( 3.6 \times 10^{20} \), which is option (C).