Question

Two ions $A^{+}$ and $B^{-}$ have radii 88pm and 200pm, respectively. In the close-packed crystal of the compound AB, predict the coordination number of $A^{+}$

• A. 6
• B. 7
• C. 5
• D. 4

Answer 1

The correct option is A

6

Let us look at the radius ratio of the compound AB.

Here, $\frac{rc}{ra}$= radius of $\frac{A^{+}}{radius}$ of $B^{-}=\frac{88}{200}=0.44$ approximately We can see that 0.44 lies in the range of 0.414-0.732. But don’t we already know what kind of void is the cation in if the radius ratio is 0.414-0.732? An octahedral void right?

Now I have an octahedral void. How many ions surround an ion in an octahedral void? 6 isn’t it? So, the coordination number would be 6.

Note: Instead of going through all this thought process, keep in mind that chart provided for coordination number and radius ratios ranges. You can quickly map the radius ratio to the appropriate coordination number.