Question

KC1 has the NaCl type structure which is fcc with two-atom basis, one at \( (0, 0, 0) \) and the other at \( \left( \frac{1}{2}, \frac{1}{2}, \frac{1}{2} \right) \). Assume that the atomic form factors of \( K^+ \) and \( Cl^- \) are identical. In an x-ray diffraction experiment on KC1, which of the following \( (h k l) \) peaks will be observed?

• A. \( (1 0 0) \)
• B. \( (1 1 0) \)
• C. \( (1 1 1) \)
• D. \( (2 0 0) \)

Hint:

For fcc crystals, diffraction peaks occur when \( h + k + l \) is even.

Answer 1

The Correct Option is C

Step 1: Understanding the diffraction condition.
In x-ray diffraction, the observed peaks correspond to diffraction conditions where the diffraction condition \( 2d \sin \theta = n\lambda \) is satisfied. For an fcc structure with two atoms in the basis, the allowed diffraction peaks occur when \( h + k + l \) is an even number, and the \( (1 1 1) \) peak satisfies this condition.
Step 2: Conclusion.
Therefore, the correct answer is option (C) because \( (1 1 1) \) is the allowed peak.