Four absorption lines measured in the fundamental ( ) infrared band of carbon…

PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · Molecular structure and spectra · Molecular structure and spectra

Reading the Spectrum, Ch Two nuclei on one curve: rotation, vibration and the spectrum of a diatomic molecule

Problem

Four absorption lines measured in the fundamental (

v=0\to1

) infrared band of carbon monoxide (CO), the four nearest the centre of the band, are quoted to the nearest

0.1\,\mathrm{cm^{-1}}

and listed here in no particular order:

2151.0

2135.6

2147.2

2139.4\,\mathrm{cm^{-1}}

. ((a)) Lines within the

R

branch (

\Delta J = +1

) and within the

P

branch (

\Delta J = -1

) are each spaced by

2B_0

, and the two lines nearest the empty centre of the band are

R(0)

and

P(1)

, which are

4B_0

apart. Use this to assign each of the four lines to its branch and its starting rotational quantum number

J

. ((b)) Hence find the rotational constant

B_0

and the band origin

\tilde\nu_0

of this band.

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