`H_2O` has net dipole moment while `BeF_2` has zero dipole moment because

Options

A. `H_2O` molecule is linear while `BeF_2` is bent
B. `BeF_2` molecule is linear while `H_2O`is bent
C. fluorine has more electronegativity than oxygen
D. beryllium has more electronegativity than oxygen

Explanation

To understand why \( H_2O \) has a net dipole moment while \( BeF_2 \) has zero dipole moment, we can analyze the molecular geometry and electronegativity of the atoms involved.

### Step-by-Step Solution:

1. **Identify the Central Atom and Valence Electrons:**
- For \( H_2O \), the central atom is Oxygen (O), which has 6 valence electrons. There are 2 Hydrogen (H) atoms, each contributing 1 valence electron.
- Total for \( H_2O \): \( 6 + 2 = 8 \) valence electrons.

2. **Determine Hybridization for \( H_2O \):**
- Using the formula for hybridization:
\[ \text{Hybridization} = \frac{1}{2} \left( \text{Number of valence electrons on central atom} + \text{Number of monovalent atoms} - \text{Charge} \right) \]
- For \( H_2O \):
\[ \text{Hybridization} = \frac{1}{2} (6 + 2 - 0) = 4 \quad \text{(SP}^3\text{ hybridization)} \]

3. **Draw the Molecular Geometry of \( H_2O \):**
- \( H_2O \) has 2 bond pairs and 2 lone pairs, resulting in a bent shape due to the repulsion between lone pairs.

4. **Analyze the Dipole Moment in \( H_2O \):**
- Oxygen is more electronegative than Hydrogen, creating a dipole moment directed towards Oxygen. Since the molecule is bent, the dipoles do not cancel out, resulting in a net dipole moment.

5. **Now, Analyze \( BeF_2 \):**
- The central atom is Beryllium (Be), which has 2 valence electrons. There are 2 Fluorine (F) atoms, each contributing 1 valence electron.
- Total for \( BeF_2 \): \( 2 + 2 = 4 \) valence electrons.

6. **Determine Hybridization for \( BeF_2 \):**
- For \( BeF_2 \):
\[ \text{Hybridization} = \frac{1}{2} (2 + 2 - 0) = 2 \quad \text{(SP hybridization)} \]

7. **Draw the Molecular Geometry of \( BeF_2 \):**
- \( BeF_2 \) has 2 bond pairs and no lone pairs, resulting in a linear shape.

8. **Analyze the Dipole Moment in \( BeF_2 \):**
- Fluorine is more electronegative than Beryllium, creating dipoles directed towards each Fluorine atom. However, since the molecule is linear, the dipoles cancel each other out, resulting in a net dipole moment of zero.

### Conclusion:
- \( H_2O \) has a net dipole moment due to its bent shape and the presence of lone pairs that prevent dipole cancellation.
- \( BeF_2 \) has zero dipole moment because it is linear, and the dipoles from the two \( Be-F \) bonds cancel each other out.