Limiting radius ratio `((r_(+))``/``(r_(-)))` for co-ordination number six (octahedral arrangement ) is

Options

A. 0.155-0.225
B. 0.225-0.414
C. 0.414-0.732
D. 0.732-1.000

Explanation

To find the limiting radius ratio \( \left( \frac{r_{+}}{r_{-}} \right) \) for coordination number six (octahedral arrangement), we can follow these steps:

### Step 1: Understand the Coordination Number
The coordination number refers to the number of nearest neighbor atoms or ions surrounding a central atom or ion. For octahedral coordination, the coordination number is six.

### Step 2: Identify the Limiting Radius Ratio
The limiting radius ratio \( \left( \frac{r_{+}}{r_{-}} \right) \) is defined as the ratio of the radius of the cation \( r_{+} \) to the radius of the anion \( r_{-} \).

### Step 3: Reference the Given Ranges
From the information provided, we have the following ranges for the limiting radius ratio based on coordination numbers:
- Coordination number 3: \( 0.155 \) to \( 0.225 \)
- Coordination number 4: \( 0.225 \) to \( 0.414 \)
- Coordination number 6: \( 0.414 \) to \( 0.732 \)
- Coordination number 8: \( 0.732 \) to \( 1.0 \)

### Step 4: Extract the Relevant Range
For coordination number six (octahedral arrangement), the limiting radius ratio \( \left( \frac{r_{+}}{r_{-}} \right) \) is in the range of \( 0.414 \) to \( 0.732 \).

### Step 5: Conclusion
Thus, the limiting radius ratio \( \left( \frac{r_{+}}{r_{-}} \right) \) for coordination number six is \( 0.414 \) to \( 0.732 \).

### Final Answer
The limiting radius ratio for coordination number six (octahedral arrangement) is \( 0.414 \leq \frac{r_{+}}{r_{-}} \leq 0.732 \).

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