The radius of `Na^(+)` ion is 95 pm and that of `Cl^(-)` ion is 181 pm. Predict the structure of `Na^(+)Cl^(-)` and the coordination number of cation.

Explanation

To solve the problem, we need to determine the structure of NaCl and the coordination number of the cation \( Na^+ \). Here are the steps to arrive at the solution:

### Step 1: Identify the ionic radii
The radius of the \( Na^+ \) ion is given as 95 pm, and the radius of the \( Cl^- \) ion is given as 181 pm.

### Step 2: Calculate the ratio of the ionic radii
We calculate the ratio of the radius of the cation to the radius of the anion:
\[ \text{Ratio} = \frac{r_{Na^+}}{r_{Cl^-}} = \frac{95 \, \text{pm}}{181 \, \text{pm}} \approx 0.524 \]

### Step 3: Determine the coordination number
To determine the coordination number based on the ratio calculated, we refer to the general rules for coordination numbers in ionic compounds:
- A ratio between 0.732 and 0.414 typically indicates an octahedral coordination.
- Since our ratio of 0.524 lies between these two values, we can conclude that the coordination number for \( Na^+ \) in \( NaCl \) is 6.

### Step 4: Predict the structure of NaCl
The structure of \( NaCl \) is based on a face-centered cubic (FCC) lattice. In this structure, each \( Na^+ \) ion is surrounded by 6 \( Cl^- \) ions, and each \( Cl^- \) ion is surrounded by 6 \( Na^+ \) ions, confirming the octahedral coordination.

### Conclusion
Thus, the structure of \( NaCl \) is face-centered cubic (FCC), and the coordination number of the cation \( Na^+ \) is 6.

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