Introduction:
The dipole moment of a molecule is a measure of the separation of positive and negative charges within the molecule. It is a vector quantity, indicating both magnitude and direction. The dipole moment of a molecule depends on the difference in electronegativity between its constituent atoms and the molecular geometry. In the case of ozone (O3) molecule, it has an unusually low dipole moment, which can be explained by considering its molecular structure and the distribution of charges.

Molecular Structure of Ozone:
Ozone (O3) is a bent molecule that consists of three oxygen atoms. The central oxygen atom is doubly bonded to the two terminal oxygen atoms, resulting in a resonance hybrid structure. The molecular geometry of ozone is trigonal planar with a bond angle of approximately 117 degrees. This bent shape is a result of electron repulsion and the desire to minimize electron-electron repulsion in the molecule.

Key Points:
The unusually low dipole moment of the ozone molecule can be explained by the following factors:

1. Symmetry:
- Ozone molecule exhibits a high degree of symmetry due to its trigonal planar geometry.
- The two O-O bond dipoles within the molecule are equal in magnitude but opposite in direction.
- As a result, the individual dipole moments of the O-O bonds cancel each other out, resulting in a net dipole moment close to zero.

2. Equal electronegativity:
- Oxygen atoms have similar electronegativities, so there is no significant difference in electron distribution between the oxygen atoms.
- This means that the oxygen atoms do not have a strong inherent polarity, leading to a low dipole moment for the molecule.

3. Resonance:
- The resonance hybrid structure of ozone contributes to the cancellation of dipole moments.
- The delocalization of electrons through resonance results in a more uniform distribution of charges, reducing the overall dipole moment.

Conclusion:
In conclusion, the unusually low dipole moment of the ozone molecule can be attributed to its molecular structure and the distribution of charges. The symmetry of the molecule and the cancellation of dipole moments between the O-O bonds play a significant role in reducing the net dipole moment. Additionally, the equal electronegativity of the oxygen atoms and the resonance hybrid structure further contribute to the low dipole moment of ozone.