Daily answer writing · Fri, 13 Nov, 2026
Microwave spectrum of CO: bond length from the line spacing, and the effect of ¹³C
The pure rotational spectrum of 12C16O shows lines spaced 3.8424 cm−1 apart.
(a) Calculate the rotational constant $B$, the moment of inertia and the C–O bond length.
(b) Predict the wavenumber of the $J = 3 \leftarrow 2$ line, the line spacing for 13C16O (same bond length), and the $J$ value of the most populated rotational level at 300 K.
(c) Why do H2 and CO2 show no pure rotational spectrum?
(12C = 12.0000, 13C = 13.0034, 16O = 15.9949 u; 1 u = $1.6605\times10^{-27}$ kg; $h = 6.626\times10^{-34}$ J s; $c = 2.998\times10^{10}$ cm s−1; $k = 1.381\times10^{-23}$ J K−1)
Syllabus: Common to CSE Paper I, IFoS Paper I and Geo-Scientist Mains (physical/spectroscopy): rotational (microwave) spectra of diatomic molecules, rigid rotor, selection rules, isotope effect, determination of bond length.
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