The greater the value of `r_(+)//r_(-)`.

Options

A. The lower will be the CN
B. The higher the value of CN
C. The higher will be the number of cations
D. The lower will be the number of anions

Answer

To solve the question regarding the relationship between the radius ratio \( r_{(+)} / r_{(-)} \) and the coordination number in ionic solids, we can follow these steps:

### Step 1: Understand the Radius Ratio
The radius ratio \( r_{(+)} / r_{(-)} \) is defined as the ratio of the radius of the cation (positive ion) to the radius of the anion (negative ion). This ratio helps in determining the coordination number of the ions in a crystal lattice.

### Step 2: Analyze the Coordination Number
The coordination number refers to the number of nearest neighbors surrounding a central atom or ion in a crystal structure. For ionic compounds, the coordination number is influenced by the size of the cations and anions.

### Step 3: Examine the Radius Ratio Ranges
Based on the information provided in the video transcript, we can summarize the relationship between the radius ratio and the coordination number:

- If \( 0.155 < \frac{r_{(+)}}{r_{(-)}} < 0.225 \), then the coordination number is 3.
- If \( 0.225 < \frac{r_{(+)}}{r_{(-)}} < 0.414 \), then the coordination number is 4.
- If \( 0.414 < \frac{r_{(+)}}{r_{(-)}} < 0.732 \), then the coordination number is 6.
- If \( 0.732 < \frac{r_{(+)}}{r_{(-)}} < 1 \), then the coordination number is 8.

### Step 4: Draw Conclusions
From the above ranges, we can conclude that as the radius ratio \( r_{(+)} / r_{(-)} \) increases, the coordination number also increases. Therefore, the statement "The greater the value of \( r_{(+)} / r_{(-)} \), the higher the coordination number" is true.

### Final Answer
The greater the value of \( r_{(+)} / r_{(-)} \), the higher the coordination number.

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