Question

The ionic radii of $A^+$ and $B^-$ ions are $0.98 \times 10^{-10} \, m$ and ${1.81 \times 10^{-10} m}$. The coordination number of each ion in AB is :

• A. 4
• B. 8
• C. 2
• D. 6

Answer 1

The Correct Option is D

The question asks us to determine the coordination number of each ion in the compound AB given the ionic radii of A^+ and B^− ions.

The ionic radii provided are:

• A^+: 0.98 \times 10^{-10} \, \text{m}
• B^−: 1.81 \times 10^{-10} \, \text{m}

The coordination number is typically determined by the radius ratio of the cation to the anion, which is given by:

r = \frac{r_{A^+}}{r_{B^-}}

Substituting the given values, we calculate:

r = \frac{0.98 \times 10^{-10}}{1.81 \times 10^{-10}} \approx 0.54

The radius ratio rule suggests the following coordination numbers for specific ranges:

• If r \lt 0.155, coordination number is 2
• If 0.155 \le r \lt 0.225, coordination number is 3
• If 0.225 \le r \lt 0.414, coordination number is 4
• If 0.414 \le r \lt 0.732, coordination number is 6
• If r \ge 0.732, coordination number is 8

Since our calculated radius ratio 0.54 lies in the range 0.414 \le r \lt 0.732, the coordination number is 6.

Thus, the correct answer is:

6