Concept:The radius ratio rule predicts the coordination number and resulting local geometric shape of an ionic crystal based on the relative sizes of the cation and anion.
Formula:$$ \text{Radius Ratio} = \frac{r^+}{r^-} $$
Solution:- For sodium chloride (\( \text{NaCl} \)), the radius ratio of the sodium cation to the chloride anion is approximately \( \frac{r_+}{r_-} = 0.52 \).
- According to standard crystallographic rules, a radius ratio falling exactly between 0.414 and 0.732 dictates a coordination number of 6.
- A coordination number of 6 corresponds geometrically to an octahedral spatial arrangement, where each ion sits in the center of an octahedron formed by 6 oppositely charged neighbors.
Why other options are incorrect:- B: Body Centered Cubic requires a coordination number of 8 (radius ratio 0.732 to 1.0).
- C: Tetrahedral requires a coordination number of 4 (radius ratio 0.225 to 0.414).
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