Question

A solid is formed of two different elements, A and B. In this atoms of A are arranged in the CCP array, and atoms of B occupy all octahedral voids and half of tetrahedral voids. Find the formula of the solid.

• A. \(\text{AB}\)
• B. \(\text{A}_{2}\text{B}\)
• C. \(\text{AB}_{2}\)
• D. \(\text{AB}_{3}\)

Hint:

In a ccp array of N atoms there are N octahedral and 2N tetrahedral voids.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
In a close-packed array of N atoms, there are N octahedral voids and 2N tetrahedral voids.

Step 2: Count the atoms
Let A atoms in ccp = \(N\).
Octahedral voids \(=N\) and tetrahedral voids \(=2N\).

Step 3: B atoms
B occupies all octahedral voids, so \(N\) atoms, plus half the tetrahedral voids, \(\dfrac{2N}{2}=N\) atoms.
Total B \(=N+N=2N\).

Step 4: Formula
A : B = \(N:2N=1:2\), so the formula is \(\text{AB}_{2}\).

Final Answer:
The formula of the solid is AB2. \[ \boxed{\text{(C) }\text{AB}_{2}} \]