Rotational Spectra of Diatomic Molecules: 20 flashcards
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1. What is a rotational spectrum?
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Absorption or emission of radiation caused by a molecule changing its rotational energy level.
2. In which region of the electromagnetic spectrum do pure rotational spectra mainly lie?
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Microwave and far-infrared regions.
3. What is the rigid rotor model?
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A model treating a diatomic molecule as two masses joined by a fixed-length rod with no stretching or bending.
4. Write the formula for moment of inertia of a diatomic molecule.
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$I = \mu r^2$
5. Define reduced mass $\mu$ for a diatomic molecule.
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$\mu = \dfrac{m_1 m_2}{m_1 + m_2}$
6. Write the rotational energy level expression for a rigid rotor.
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$E_J = hcB\,J(J+1)$, with $J = 0, 1, 2, \dots$
7. Define the rotational constant $B$.
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$B = \dfrac{h}{8\pi^2 c I}$, usually expressed in cm$^{-1}$.
8. State the selection rule for a rigid rotor.
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$\Delta J = \pm 1$
9. At what wavenumbers do allowed rigid-rotor transitions appear?
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$2B, 4B, 6B, \dots$ — equally spaced by $2B$.
10. What does the line spacing in a rotational spectrum directly give?
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The rotational constant $B$ (spacing $= 2B$).
11. What condition must a molecule satisfy to show a pure rotational spectrum?
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It must possess a permanent dipole moment.
12. Why do H$_2$ and N$_2$ show no pure rotational spectrum?
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They are homonuclear diatomics with no permanent dipole moment, so they are microwave-inactive.
13. Why does CO$_2$ lack a pure rotational spectrum?
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It has no permanent dipole moment (linear and symmetric), so it is microwave-inactive.
14. Name three molecules that are microwave-active.
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HCl, CO and H$_2$O — all possess permanent dipole moments.
15. What causes centrifugal distortion in rotational spectra?
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The bond stretches slightly as rotation speeds up, so lines bunch up at high $J$.
16. What is the lowest-frequency line in a rigid-rotor spectrum?
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The $J = 0 \to 1$ transition, at $2B$.
17. How does rotational spectroscopy give bond lengths?
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Measure line spacing $2B$ → get $B$ → get $I$ → get $r = \sqrt{I/\mu}$.
18. Give one real-world application of rotational spectroscopy.
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Identifying molecules in interstellar space by their microwave fingerprints.
19. How does increasing $J$ affect the energy gap between adjacent levels?
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The gap increases with $J$ (gap $= 2hcB(J+1)$).
20. Why do different isomers give different rotational spectra?
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They have different moments of inertia, hence different $B$ values and line spacings.
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