Question
Consider the following six vibrational modes:
symmetric stretching of $CO_2$, O-H symmetric stretching of $H_2O$, stretching of HCl, stretching of $H_2$, N-H symmetric stretching of $NH_3$, and bending of $CO_2$.
Among these modes, if k number of modes are IR active but Raman inactive, l number of modes are IR inactive but Raman active, and m number of modes are both IR and Raman active.
k, l, and m, respectively, are
The correct answer is
1, 2, and 3
Molecular Vibrational Mode Activity Analysis
Understanding the conditions for Infrared (IR) and Raman activity is crucial for analyzing molecular vibrations.
- IR Activity: A vibrational mode is IR active if it causes a change in the molecule's dipole moment.
- Raman Activity: A vibrational mode is Raman active if it causes a change in the molecule's polarizability.
Vibrational Mode Classification Table
We analyze the six given vibrational modes:
| Vibrational Mode | Molecule | Symmetry (Example) | Dipole Moment Change | Polarizability Change | IR Activity | Raman Activity |
|---|---|---|---|---|---|---|
| Symmetric stretching | $CO_2$ | $D_{\infty h}$ | No | Yes | Inactive | Active |
| O-H symmetric stretching | $H_2O$ | $C_{2v}$ | Yes | Yes | Active | Active |
| Stretching | HCl | $C_{\infty v}$ | Yes | Yes | Active | Active |
| Stretching | $H_2$ | $D_{\infty h}$ | No | Yes | Inactive | Active |
| N-H symmetric stretching | $NH_3$ | $C_{3v}$ | Yes | Yes | Active | Active |
| Bending | $CO_2$ | $D_{\infty h}$ | Yes | No | Active | Inactive |
Calculating k, l, and m Values
Based on the table, we count the modes:
- k: IR active but Raman inactive
- Bending of $CO_2$ (1 mode)
So, $k = 1$. - l: IR inactive but Raman active
- Symmetric stretching of $CO_2$
- Stretching of $H_2$
(2 modes)
So, $l = 2$. - m: Both IR and Raman active
- O-H symmetric stretching of $H_2O$
- Stretching of HCl
- N-H symmetric stretching of $NH_3$
(3 modes)
So, $m = 3$.
Therefore, k, l, and m are 1, 2, and 3, respectively.
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Important Questions from Spectroscopy
- If a molecule emitting a radiation of frequency $3.100 \times 10^9 \text{ Hz}$ approaches an observer with a relative speed of $5.000 \times 10^6 \text{ m s}^{-1}$, then the observer detects a frequency of ________ $\times 10^9 \text{ Hz}$. (rounded off to three decimal places)
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