Molecular spectra: rotational, vibrational and electronic
Atomic and molecular spectra · Physics
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Interactive 3DBall-and-stick models with true bond angles — switch molecule to compare shapes.
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Study notes
Worked example - bond length of carbon monoxide from its microwave spectrum. CO's rotational lines are spaced by 2B with B = 1.93 cm^-1. Step 1: the J=0->1 line is at 3.86 cm^-1, i.e. wavelength 2.59 mm (microwave). Step 2: convert B to Hz: B = 1.93 x 100 x c = 5.79 x 10^10 Hz. Moment of inertia I = h/(8 pi^2 B) = 6.626 x 10^-34/(8 x 9.87 x 5.79 x 10^10) = 1.45 x 10^-46 kg.m^2. Step 3: reduced mass of CO: mu = (12 x 16)/(12+16) amu = 6.86 amu = 1.14 x 10^-26 kg. Bond length r = sqrt(I/mu) = sqrt(1.45 x 10^-46/1.14 x 10^-26) = 1.13 x 10^-10 m = 1.13 angstrom - the accepted CO bond length.