Explanation:

To determine the number of lone pairs of electrons on the central atom in I3-, ClF3, and ClO3-, we need to consider the Lewis structures of these molecules and ions.

I3-:
- I3- consists of three iodine atoms bonded together with a single negative charge. The central atom in this case is one of the iodine atoms.
- Each iodine atom has 7 valence electrons.
- The three iodine atoms are bonded together using two covalent bonds, each sharing two electrons.
- To complete the octet of each iodine atom, there must be six additional electrons.
- The negative charge on the ion indicates the presence of one extra electron.
- Hence, the central iodine atom has 7 (valence electrons) + 6 (shared electrons) + 1 (extra electron) = 14 electrons in total.
- Subtracting the shared electrons (4) from the total number of electrons gives us the number of lone pairs on the central atom.
- Therefore, the central iodine atom in I3- has 14 - 4 = 10 lone pairs of electrons.

ClF3:
- ClF3 consists of one central chlorine atom surrounded by three fluorine atoms.
- Chlorine has 7 valence electrons, and each fluorine atom has 7 valence electrons.
- The three fluorine atoms are bonded to the central chlorine atom using three covalent bonds, each sharing two electrons.
- To complete the octet of the central chlorine atom, there must be two additional electrons.
- Therefore, the central chlorine atom has 7 (valence electrons) + 6 (shared electrons) + 2 (extra electrons) = 15 electrons in total.
- Subtracting the shared electrons (6) from the total number of electrons gives us the number of lone pairs on the central atom.
- Therefore, the central chlorine atom in ClF3 has 15 - 6 = 9 lone pairs of electrons.

ClO3-:
- ClO3- consists of one central chlorine atom bonded to three oxygen atoms with a single negative charge.
- Chlorine has 7 valence electrons, and each oxygen atom has 6 valence electrons.
- The three oxygen atoms are bonded to the central chlorine atom using three covalent bonds, each sharing two electrons.
- To complete the octet of the central chlorine atom, there must be one additional electron.
- The negative charge on the ion indicates the presence of one extra electron.
- Therefore, the central chlorine atom has 7 (valence electrons) + 6 (shared electrons) + 1 (extra electron) = 14 electrons in total.
- Subtracting the shared electrons (6) from the total number of electrons gives us the number of lone pairs on the central atom.
- Therefore, the central chlorine atom in ClO3- has 14 - 6 = 8 lone pairs of electrons.

Conclusion:
- The number of lone pairs on the central atom in I3-, ClF3, and ClO3- are 10, 9, and 8, respectively.
- Hence, the correct answer is '6'.