The question pertains to the structural characteristics of the NaCl crystal and asks which of the given options is mismatched. Let's analyze each option to determine the correct answer:
- \(\frac{r^+}{r^-} = 0.414 \text{ to } 0.732\): This is the range of radius ratio for octahedral coordination, which is the case in NaCl. Here, \(r^+\) and \(r^−\) refer to the radii of the cation and anion respectively. This option is correctly matched.
- Coordination number = \(6:6\): In NaCl, each Na+ ion is surrounded by six Cl− ions and vice versa, resulting in a coordination number of 6, which is accurate. Hence, this option is also correctly matched.
- Edge of unit cell = \(r^+ + r^-\): In an NaCl structure (which is an FCC lattice with Na+ and Cl− alternating), the edge length \(a\) is actually related to the radii of the ions by the formula: \(a = 2(r^+ + r^-)\). Hence, stating it as \(r^+ + r^−\) is incorrect as the edge length is not equal to the sum of the ionic radii, but involves a factor of 2. Thus, this option is mismatched.
- Crystal structure = fcc: The NaCl crystal structure is indeed face-centered cubic (fcc). Therefore, this option is properly matched.
Based on the above analysis, the mismatched statement is: Edge of unit cell = \(r^+ + r^−\).