A mineral having the formula `AB_(2)` crytallises in the cubic close-packed lattice, with the A atoms occupying the lattice points. What is the coordination number of the A atoms and B atoms ? What percentage fraction of the tetrahedral sites is occupied by B atoms ?

Explanation

To solve the problem, we will analyze the cubic close-packed (CCP) lattice structure and the coordination numbers of the A and B atoms, as well as the percentage of tetrahedral sites occupied by B atoms.

### Step 1: Understanding the Structure
In a cubic close-packed (CCP) lattice, the A atoms occupy the lattice points. In this case, the mineral has the formula AB₂, indicating that for every one A atom, there are two B atoms.

### Step 2: Coordination Number of A Atoms
The coordination number of an atom is defined as the number of nearest neighboring atoms surrounding it. In a CCP structure:
- Each A atom at the lattice points is surrounded by 12 B atoms (since there are 2 B atoms for every A atom).
...