Select the correct statement regarding shapes of `PCl_(5), BrF_(5)` & `IF_(7)` :

Options

A. All are square pyramidal
B. All are trigonal bipyramidal
C. One of the following is square pyramidal
D. one of the following is tetrahedral

Explanation

To determine the shapes of the molecules \( PCl_5 \), \( BrF_5 \), and \( IF_7 \), we will follow a systematic approach by calculating the total number of valence electrons, determining the bond pairs and lone pairs, and then identifying the molecular geometry based on these pairs.

### Step 1: Determine the shape of \( PCl_5 \)

1. **Calculate the total number of valence electrons (V)**:
- Phosphorus (P) has 5 valence electrons.
- Each Chlorine (Cl) has 7 valence electrons, and there are 5 Chlorine atoms.
- Total \( V = 5 + (5 \times 7) = 5 + 35 = 40 \).

2. **Determine the number of bond pairs and lone pairs**:
- Divide \( V \) by 8: \( \frac{40}{8} = 5 \) (quotient) and remainder is 0.
- Number of bond pairs = 5, Number of lone pairs = 0.

3. **Identify the shape**:
- With 5 bond pairs and no lone pairs, \( PCl_5 \) has a **trigonal bipyramidal** shape.

### Step 2: Determine the shape of \( BrF_5 \)

1. **Calculate the total number of valence electrons (V)**:
- Bromine (Br) has 7 valence electrons.
- Each Fluorine (F) has 7 valence electrons, and there are 5 Fluorine atoms.
- Total \( V = 7 + (5 \times 7) = 7 + 35 = 42 \).

2. **Determine the number of bond pairs and lone pairs**:
- Divide \( V \) by 8: \( \frac{42}{8} = 5 \) (quotient) and remainder is 2.
- Number of bond pairs = 5, Number of lone pairs = 1 (since remainder is 2, which corresponds to 1 lone pair).

3. **Identify the shape**:
- With 5 bond pairs and 1 lone pair, \( BrF_5 \) has a **square pyramidal** shape.

### Step 3: Determine the shape of \( IF_7 \)

1. **Calculate the total number of valence electrons (V)**:
- Iodine (I) has 7 valence electrons.
- Each Fluorine (F) has 7 valence electrons, and there are 7 Fluorine atoms.
- Total \( V = 7 + (7 \times 7) = 7 + 49 = 56 \).

2. **Determine the number of bond pairs and lone pairs**:
- Divide \( V \) by 8: \( \frac{56}{8} = 7 \) (quotient) and remainder is 0.
- Number of bond pairs = 7, Number of lone pairs = 0.

3. **Identify the shape**:
- With 7 bond pairs and no lone pairs, \( IF_7 \) has a **pentagonal bipyramidal** shape.

### Summary of Shapes:
- \( PCl_5 \): Trigonal bipyramidal
- \( BrF_5 \): Square pyramidal
- \( IF_7 \): Pentagonal bipyramidal

### Conclusion:
The correct statement regarding the shapes of \( PCl_5 \), \( BrF_5 \), and \( IF_7 \) is that **one of the following is square pyramidal**, which refers to \( BrF_5 \).