If the ratio of coordination no. of A to that iof B is x:y, then the ratio of no. of atoms of A to that no, of atoms of B in the unit cell is

Options

A. x:y
B. y:x
C. `x^(2):y`
D. `y:x^(2)`

Answer

To solve the problem, we need to find the ratio of the number of atoms of A to the number of atoms of B in a unit cell, given the ratio of their coordination numbers.

### Step-by-Step Solution:

1. **Understand Coordination Number**:
- The coordination number (CN) of an atom in a crystal structure is the number of nearest neighboring atoms surrounding it.
- In this case, we are given that the coordination number of A is \( x \) and that of B is \( y \).

2. **Set Up the Relationship**:
- Since the coordination number of A is \( x \), it means that each atom of A is surrounded by \( x \) atoms of B.
- Similarly, since the coordination number of B is \( y \), each atom of B is surrounded by \( y \) atoms of A.

3. **Express Number of Atoms**:
- Let’s denote the number of atoms of A in the unit cell as \( n_A \) and the number of atoms of B as \( n_B \).
- From the coordination numbers, we can express:
- The number of atoms of A in terms of B: \( n_A = n \cdot y \) (where \( n \) is a constant).
- The number of atoms of B in terms of A: \( n_B = n \cdot x \).

4. **Formulate the Ratio**:
- Now, we can find the ratio of the number of atoms of A to the number of atoms of B:
\[ \frac{n_A}{n_B} = \frac{n \cdot y}{n \cdot x} = \frac{y}{x} \]

5. **Final Result**:
- Therefore, the ratio of the number of atoms of A to the number of atoms of B in the unit cell is \( \frac{y}{x} \).

### Conclusion:
The final answer is that the ratio of the number of atoms of A to the number of atoms of B in the unit cell is \( y : x \).

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