Predict coordination umber of the cation in crystals of the following compounds :
`(1). MgO:r_(c)=0.65Å, r_(a)=1.40Å`
`(2). MgS:r_(c)=0.65Å, r_(a)=1.84Å`

Options

A. 6,4
B. 4,6
C. 3,4
D. 6,8

Answer

To predict the coordination number of the cation in the crystals of the given compounds (MgO and MgS), we will use the radius ratio rule. This rule helps us determine the type of voids occupied by cations based on the ratio of the radius of the cation to the radius of the anion.

### Step-by-Step Solution:

**1. Calculate the radius ratio for MgO:**
- Given:
- Radius of cation (Mg²⁺), \( r_c = 0.65 \) Å
- Radius of anion (O²⁻), \( r_a = 1.40 \) Å
- Radius ratio \( R = \frac{r_c}{r_a} = \frac{0.65}{1.40} \)
- Calculate \( R \):
\[ R = \frac{0.65}{1.40} \approx 0.464 \]

**2. Determine the coordination number for MgO:**
- The radius ratio \( R \approx 0.464 \) falls within the range of \( 0.414 < R < 0.732 \).
- According to the radius ratio rule, if \( R \) is in this range, the cation occupies an octahedral void.
- Therefore, the coordination number of the cation in MgO is **6**.

**3. Calculate the radius ratio for MgS:**
- Given:
- Radius of cation (Mg²⁺), \( r_c = 0.65 \) Å
- Radius of anion (S²⁻), \( r_a = 1.84 \) Å
- Radius ratio \( R = \frac{r_c}{r_a} = \frac{0.65}{1.84} \)
- Calculate \( R \):
\[ R = \frac{0.65}{1.84} \approx 0.353 \]

**4. Determine the coordination number for MgS:**
- The radius ratio \( R \approx 0.353 \) falls within the range of \( 0.225 < R < 0.414 \).
- According to the radius ratio rule, if \( R \) is in this range, the cation occupies a tetrahedral void.
- Therefore, the coordination number of the cation in MgS is **4**.

### Final Answer:
- For MgO, the coordination number of the cation is **6**.
- For MgS, the coordination number of the cation is **4**.