Step 1: Understanding the Concept:
The octet rule states that atoms are most stable when their valence shell contains eight electrons.
However, elements from the 3rd period onwards have vacant d-orbitals and can accommodate more than 8 electrons, leading to an "expanded octet."
Step 3: Detailed Explanation:
Analyze the central atoms:
(A) Ozone (\(O_3\)): Oxygen is in the 2nd period; it follows the octet rule.
(B, C) NO and \(NO_2\): Nitrogen is in the 2nd period. These are odd-electron molecules, but they cannot expand their octet.
(D) Water (\(H_2O\)): Oxygen has 8 electrons (octet).
(E) Sulphur hexafluoride (\(SF_6\)): Sulphur (Group 16) is in the 3rd period. It has 6 valence electrons. In \(SF_6\), it shares all 6 electrons to form 6 single bonds with Fluorine.
Total electrons around Sulphur = \(6 \text{ bonds} \times 2 = 12\) electrons.
Since 12 \(>\) 8, it is an expanded octet.
Step 4: Final Answer:
Sulphur hexafluoride is the molecule with an expanded octet.