# Spectroscopy 1: Rotational and Vibrational Spectra CHAPTER 13.

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Spectroscopy 1: Rotational and Vibrational Spectra CHAPTER 13

The Electromagnetic Spectrum

Fig 13.2 (a) Schematic of a typical absorption spectrophotometer

Constructive and destructive interference 0°0° 180°

Principle of a diffraction grating Constructive interference when: nλ = d(sin θ – sin φ) Blue light “bends” more than red light

Effect of rotating the diffraction grating Blue red p o l y c h r o m a t i c

Schematic of a Czerny-Turner monochromator. collimating mirror focusing mirror diffraction grating

Fig 13.2 (b) Schematic of a typical emission spectrophotometer 90 o

The intensities of spectral lines Absorbance: Beer-Lambert Law: A = εbc ε ≡ molar absorptivityb ≡ path lengthc ≡ molarity

Fig 13.4 Plot of the integrated absorption coefficient of a transition A ε may not give true indication of transition intensity

Fig 13.5 Processes that account for absorption and emission of radiation Einstein coefficients : B B’ A account for absorption and emission intensities

Selection rules Classically: For a molecule to interact with the em field and absorb/emit a photon of frequency ν, it must possess (at least transiently) a dipole oscillating at ν. Known as a gross selection rule

Fig 13.6 When a 1s electron becomes a 2s electron there is no net dipole moment associated with the migration of charge Transition is electric-dipole forbidden Δ l ≠ 0 1s 2s specific selection rule:

1s Fig 13.6 (b) When a 1s electron becomes a 2p electron there is a net dipole moment associated with the migration of charge Transition is electric-dipole allowed Δ l = ± 1 2p Transition dipole: electric dipole moment operator specific selection rule:

Signal Δλ 1/2 = FWHM λ0λ0 FWHM ≡ Full Width at Half Maximum Linewidths Most common definition of linewidth:

SOURCES OF LINE BROADENING (in order of increasing effect) (1)Natural Linewidths (Uncertainty Broadening) Δ ν · Δt > 1   Because excited state lifetimes (t) are brief ( ∼ ns – μs), the uncertainty (Δt) is small and ∴ Δ ν is relatively large (2)Doppler Broadening   Wavelength shift caused by motion of atoms relative to detector

The Doppler Effect Blue shift Red shift

Fig 13.7 Gaussian shape of a Doppler-broadened spectral line reflect distribution of speeds as a function of temperature Line broadening increases with T Sharpest lines at low T

(3)Pressure Broadening (Collisional Broadening)   Collisions cause small changes in ground state energy levels (i.e., “smearing”)   Δλ 1/2 >> Δλ 1/2 of isolated atom   At high pressures  continuum radiation   e.g., high-pressure Hg and Xe lamps

Box 13.8 Rotational spectrum of the Orion nebula 1.44 mm1.30 mm Microwave region