A cubic solid is made up of two elements P and Q . Atoms of P are present at the corners of the cube and atoms of Q are present at body centre. What is the formula of the compound and what are coordination numbers of P and Q ?

Options

A. `PQ_2`, 6:6
B. PQ,6:6
C. `P_2Q`,6:6
D. PQ,8:8

Explanation

To solve the problem, we need to determine the formula of the compound formed by elements P and Q, as well as their coordination numbers based on their positions in the cubic solid.

### Step 1: Calculate the number of atoms of P
Atoms of P are located at the corners of the cube. In a cube, there are 8 corners, and each corner atom is shared among 8 adjacent cubes. Therefore, the contribution of each corner atom to the cube is \( \frac{1}{8} \).

- Total contribution from P:
\[ \text{Total atoms of P} = 8 \text{ corners} \times \frac{1}{8} = 1 \]

### Step 2: Calculate the number of atoms of Q
Atoms of Q are located at the body center of the cube. There is only one body center in a cube, and it is not shared with any other cube.

- Total contribution from Q:
\[ \text{Total atoms of Q} = 1 \]

### Step 3: Determine the formula of the compound
Now that we have the total number of atoms for both elements, we can write the formula of the compound.

- The formula of the compound is:
\[ \text{Formula} = P^1Q^1 = PQ \]

### Step 4: Calculate the coordination numbers
The coordination number is defined as the number of nearest neighbors surrounding an atom.

- For atom P:
In this structure, each atom of P at the corners is surrounded by the atoms of Q at the body center. Since there is one body center atom and it is surrounded by 8 corner atoms, the coordination number of P is 8.

- For atom Q:
Each atom of Q at the body center is surrounded by the 8 corner atoms of P. Thus, the coordination number of Q is also 8.

### Final Answer
- The formula of the compound is \( PQ \).
- The coordination numbers are:
- Coordination number of P = 8
- Coordination number of Q = 8