Molecular Structure Requirements
The question asks for the correct structure of an $XY_2$ molecule based on its spectral properties: microwave activity and the presence of only P and R transitions in its vibration-rotation spectrum.
- Microwave Activity: Molecules must possess a permanent dipole moment to be active in microwave spectroscopy.
- Vibration-Rotation Spectrum: The observation of only P ($\Delta J = -1$) and R ($\Delta J = +1$) transitions, with no Q branch ($\Delta J = 0$), is characteristic of linear molecules. Bent molecules typically exhibit all three branches (P, Q, and R).
Analyzing Molecular Geometries
Based on the spectral evidence, the molecule must be linear and possess a dipole moment.
Eliminating Bent Structures
Bent $XY_2$ molecules (Options 2 and 4) generally have a dipole moment but typically show P, Q, and R branches in their vibration-rotation spectra. Since only P and R transitions are observed, bent structures are unlikely.
Evaluating Linear Structures
We consider the two possible linear structures for $XY_2$:
- Option 1: X is the central atom (Y-X-Y structure). If X and Y are atoms, this structure is typically linear and symmetric (e.g., $CO_2$, $CS_2$, $BeCl_2$). Symmetric linear molecules have no net dipole moment and are microwave inactive.
- Option 3: Y is the central atom (X-Y-X structure). This structure is linear. For it to be microwave active, it must possess a dipole moment, implying it must be asymmetric. While the formula $XY_2$ often implies symmetry (identical X atoms), this arrangement allows for linearity and potentially asymmetry, which is required for microwave activity. A classic example fitting this molecular formula and linearity is $N_2O$ (N is central, structure N-N-O, formula $X_2Y$), but considering $XY_2$ with Y central (X-Y-X), asymmetry is key for activity.
Conclusion
The molecule must be linear (due to only P and R transitions) and have a dipole moment (for microwave activity). Among the linear possibilities, the structure where Y is the central atom (X-Y-X) must be the one considered asymmetric and thus possessing a dipole moment, aligning with the observed properties.
Therefore, the correct structure is linear with Y as the central atom.
Important Questions from Rotational Spectroscopy
The spacing between the two adjacent lines of the microwave spectrum of $H^{35}Cl$ is $6.35 \times 10^{11} \text{ Hz}$. Given that the bond length of $D^{35}Cl$ is 5% greater than that of $H^{35}Cl$, the corresponding spacing for $D^{35}Cl$ is ____________ $\times 10^{11} \text{ Hz}$. (Up to two decimal places)
- The microwave spectrum of gaseous HF consists of a series of lines separated by 41.11 cm$^{-1}$. The bond length (in Å) of HF is ______ (rounded off to two decimal places).
(Given: Atomic mass (in amu): H = 1.008, F = 18.998;
1 amu = $1.661 \times 10^{-27}$ kg; $h = 6.626 \times 10^{-34}$ J s; $c = 2.998 \times 10^8$ m s$^{-1}$)
