List I | List II | ||
(P) | XeF2 | (1) | Trigonal bipyramidal and two lone pair of electrons |
(Q) | XeF4 | (2) | Tetrahedral and one lone pair of electrons |
(R) | XeO3 | (3) | Octahedral and two lone pair of electrons |
(S) | XeO3F2 | (4) | Trigonal bipyramidal and no lone pair of electrons |
(5) | Trigonal bipyramidal and three lone pair of electrons |
Step 1: Determining the Geometry and Lone Pairs of Each Xenon Compound
Step 2: Conclusion
Thus, the correct answer is (B) P-5, Q-3, R-2, S-4.
To solve the problem, we need to use the VSEPR model to determine the molecular geometries and lone pairs on xenon compounds and match them with the given options.
1. Xenon Difluoride (XeF2):
- Total electron pairs: 5 (2 bonding pairs, 3 lone pairs)
- Geometry: Trigonal bipyramidal
- Lone pairs: 3
- Corresponds to option (5) "Trigonal bipyramidal and three lone pairs".
2. Xenon Tetrafluoride (XeF4):
- Total electron pairs: 6 (4 bonding pairs, 2 lone pairs)
- Geometry: Octahedral
- Lone pairs: 2
- Corresponds to option (3) "Octahedral and two lone pairs".
3. Xenon Trioxide (XeO3):
- Total electron pairs: 4 (3 bonding pairs, 1 lone pair)
- Geometry: Tetrahedral
- Lone pairs: 1
- Corresponds to option (2) "Tetrahedral and one lone pair".
4. Xenon Oxyfluoride (XeO3F2):
- Total electron pairs: 5 (5 bonding pairs, 0 lone pairs)
- Geometry: Trigonal bipyramidal
- Lone pairs: 0
- Corresponds to option (4) "Trigonal bipyramidal and no lone pairs".
Final Matching:
P - 5, Q - 3, R - 2, S - 4
Final Answer:
Option (B)
Let $ S $ denote the locus of the point of intersection of the pair of lines $$ 4x - 3y = 12\alpha,\quad 4\alpha x + 3\alpha y = 12, $$ where $ \alpha $ varies over the set of non-zero real numbers. Let $ T $ be the tangent to $ S $ passing through the points $ (p, 0) $ and $ (0, q) $, $ q > 0 $, and parallel to the line $ 4x - \frac{3}{\sqrt{2}} y = 0 $.
Then the value of $ pq $ is