Question

A cube of any crystal A-atom placed at every corners and B-atom placed at every centre of face. The formula of compound:

• A. \(AB\)
• B. \(AB_3\)
• C. \(A_2B_2\)
• D. \(A_2B_3\)

Answer 1

The Correct Option is B

The question asks for the formula of a compound in a cube-shaped crystal structure where A-atoms are located at every corner of the cube and B-atoms are placed at the center of each face of the cube.

1. First, let's calculate the number of A-atoms per unit cell:
   • The cube has 8 corners, and there is an A-atom at each corner.
   • In a cube, each corner atom is shared by 8 adjacent unit cells. Hence, the contribution of each corner atom to a single unit cell is \( \frac{1}{8} \).
   • Therefore, total A-atoms in one unit cell = \( 8 \times \frac{1}{8} = 1 \) A-atom.
2. Next, let’s calculate the number of B-atoms per unit cell:
   • There are 6 faces on a cube, and there is a B-atom at the center of each face.
   • B-atoms located at the face centers are shared by 2 adjacent unit cells. Thus, the contribution of each face-centered atom to a single unit cell is \( \frac{1}{2} \).
   • Therefore, total B-atoms in one unit cell = \( 6 \times \frac{1}{2} = 3 \) B-atoms.
3. From the above calculations, we find that the formula for the compound is:
   • \( A_1B_3 \), which is simplified as \( AB_3 \).

Therefore, the correct answer is \( AB_3 \).

Let’s rule out the other options:

• \(AB\): Implies one B-atom for every A-atom, which does not match the calculated distribution.
• \(A_2B_2\): Implies an equal number of A and B atoms, which does not reflect the structure.
• \(A_2B_3\): Implies two A atoms and three B atoms, which doesn’t match with the calculated numbers.