Shape of the compounds `XeF_(3)^(+)` and `XeF_(5)^(+)` are respectively

Options

A. Option 1. T-shape , square pyramid
B. Option 2. Sea-saw , square pyramidal
C. Option 3. T-shaped , square pyramidal
D. Option 4. T-shaped in both

Answer

To determine the shapes of the compounds \( \text{XeF}_3^+ \) and \( \text{XeF}_5^+ \), we will analyze their hybridization and molecular geometry step by step.

### Step 1: Determine the Valence Electrons for \( \text{XeF}_3^+ \)

1. **Identify the valence electrons of xenon (Xe)**:
- Xenon is in Group 18 and has 8 valence electrons.

2. **Account for the positive charge**:
- The positive charge indicates a loss of one electron, so we have \( 8 - 1 = 7 \) valence electrons.

3. **Count the number of fluorine atoms**:
- There are 3 fluorine atoms, each contributing 1 electron (3 electrons total).

4. **Calculate the total number of electrons**:
\[ \text{Total electrons} = 7 + 3 = 10 \]

### Step 2: Determine the Hybridization of \( \text{XeF}_3^+ \)

1. **Use the formula for hybridization**:
\[ \text{Hybridization} = \frac{(\text{Number of valence electrons} + \text{Number of monovalent atoms} - \text{Charge})}{2} \]
- Here, we have:
\[ \text{Hybridization} = \frac{(7 + 3 - 1)}{2} = \frac{9}{2} = 4.5 \text{ (which indicates } sp^3d\text{)} \]

2. **Determine the shape**:
- With 3 bond pairs and 2 lone pairs, the molecular geometry is T-shaped.

### Step 3: Determine the Valence Electrons for \( \text{XeF}_5^+ \)

1. **Identify the valence electrons of xenon (Xe)**:
- Again, xenon has 8 valence electrons.

2. **Account for the positive charge**:
- The positive charge indicates a loss of one electron, so we have \( 8 - 1 = 7 \) valence electrons.

3. **Count the number of fluorine atoms**:
- There are 5 fluorine atoms, contributing 5 electrons (5 electrons total).

4. **Calculate the total number of electrons**:
\[ \text{Total electrons} = 7 + 5 = 12 \]

### Step 4: Determine the Hybridization of \( \text{XeF}_5^+ \)

1. **Use the formula for hybridization**:
\[ \text{Hybridization} = \frac{(\text{Number of valence electrons} + \text{Number of monovalent atoms} - \text{Charge})}{2} \]
- Here, we have:
\[ \text{Hybridization} = \frac{(7 + 5 - 1)}{2} = \frac{11}{2} = 6 \text{ (which indicates } sp^3d^2\text{)} \]

2. **Determine the shape**:
- With 5 bond pairs and 1 lone pair, the molecular geometry is square pyramidal.

### Final Answer

- The shape of \( \text{XeF}_3^+ \) is **T-shaped**.
- The shape of \( \text{XeF}_5^+ \) is **square pyramidal**.