a.) The spacings of the rotational fine structure lines of carbon dioxide 12C16O2 are determined from IR spectroscopy to be 0.7604 cm-1. Calculate the C=O bond length of the molecule (given masses: m(12C) = 12 amu, m(16O) = 15.9949 amu). Ans = ________ Angstromsb.) A molecule in a gas undergoes 3e+09 collisions in each second. Suppose that(i) every collision is effective in deactivating the molecule rotationally. Calculate the linewidth of rotational transitions in the molecule.   Ans = _________ MHz(ii) Suppose that 1 collisions in 10 are effective. Ans =  _______  MHz

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Asked Nov 25, 2019
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a.) The spacings of the rotational fine structure lines of carbon dioxide 12C16O2 are determined from IR spectroscopy to be 0.7604 cm-1. Calculate the C=O bond length of the molecule (given masses: m(12C) = 12 amu, m(16O) = 15.9949 amu).
 Ans = ________ Angstroms

b.) A molecule in a gas undergoes 3e+09 collisions in each second. Suppose that
(i) every collision is effective in deactivating the molecule rotationally. Calculate the linewidth of rotational transitions in the molecule.   Ans = _________ MHz
(ii) Suppose that 1 collisions in 10 are effective. Ans =  _______  MHz

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Expert Answer

Step 1

Hi there! Since you have posted multiple questions, we will answer the first question for you. If you need help with the other question, kindly post it seperaetly.

Step 2

The bond length of a molecule in IR spectroscopy is calculated using the formula :

h
|8 п? с В и
Where, R bond length
h Planck's constant 6.626x10-34 kg m2s
c speed of light = 3.0x108 m s
B wave number
reduced mass
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h |8 п? с В и Where, R bond length h Planck's constant 6.626x10-34 kg m2s c speed of light = 3.0x108 m s B wave number reduced mass

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Step 3

Given,

Spacing of the rotational fine structure lines, 2B = 0.7604 cm-1

Atomic mass of C, m1 = 12 amu

Atomic mass of O, m2 = 15.9949 amu

The rotational spectra...

2B 0.7604 cm
0.7604 cm
В -
2
B 0.3802 cm
B 38.02 m1
help_outline

Image Transcriptionclose

2B 0.7604 cm 0.7604 cm В - 2 B 0.3802 cm B 38.02 m1

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