Why `BeH_2` molecule has a zero dipole moment although the Be-H bonds are polar?

Options

A. Because of its linear geometry
B. Because of two opposite and equal dipoles
C. Both (1) and (2)
D. None of the above

Answer

To understand why the `BeH_2` molecule has a zero dipole moment despite the polar nature of its Be-H bonds, we can follow these steps:

### Step 1: Identify the Molecular Geometry
The first step is to determine the molecular geometry of `BeH_2`. Beryllium (Be) forms two bonds with hydrogen (H) atoms. Since beryllium has no lone pairs of electrons, the molecular geometry is linear.

**Hint:** Remember that the molecular shape can be determined using the VSEPR theory, which states that electron pairs (bonding and lone pairs) will arrange themselves to minimize repulsion.

### Step 2: Understand Polar Bonds
Next, we need to recognize that the Be-H bonds are indeed polar. This is due to the difference in electronegativity between beryllium and hydrogen. In a polar bond, the electron density is unevenly distributed, leading to a dipole moment pointing from the less electronegative atom (Be) to the more electronegative atom (H).

**Hint:** Recall that a polar bond occurs when there is a significant difference in electronegativity between the two atoms involved in the bond.

### Step 3: Analyze the Dipole Moments
In the `BeH_2` molecule, there are two polar Be-H bonds. Each bond has a dipole moment that points towards the hydrogen atoms. However, because the molecule is linear, the dipole moments of the two bonds are equal in magnitude but opposite in direction.

**Hint:** Visualize the dipole moments as arrows pointing from Be to H. In a linear arrangement, these arrows will cancel each other out.

### Step 4: Conclusion on the Net Dipole Moment
Since the dipole moments are equal in magnitude and opposite in direction, they cancel each other out. Therefore, the net dipole moment of the `BeH_2` molecule is zero.

**Hint:** Remember that dipole moments are vector quantities; when two vectors of equal magnitude point in opposite directions, they sum to zero.

### Final Answer
The `BeH_2` molecule has a zero dipole moment because the two polar Be-H bonds have equal and opposite dipole moments that cancel each other out due to the linear geometry of the molecule.