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360 11MOLECULAR SPECTROSCOPY
1.0 1.2 1.4 1.6 1.8 2.0
2.5
3.0
3.5
4.0
ρ
I/
m
A
R
2
I∣∣
I� α = 1
I� α = .2
I� α = 5
Figure 11.3
E11B.3(b) To be a symmetric rotor a molecule most possess an n-fold axis with n > 2. (i)
Ethene has three two-fold axes, but no axes with n > 2 and so is an asymmetric
rotor. (ii) SO3 is trigonal planar; it has a three-fold axis and so is a symmetric
rotor. (iii) ClF3 is ‘T-shaped’ and has a two-fold axis; it is an asymmetric rotor.
(iv) N2O is a linear rotor.
E11B.4(b) In order to determine two unknowns, data from two independent experiments
are needed. In this exercise two values of B for two isotopologues of OCS are
given; these are used to �nd two moments of inertia.�e moment of inertia of
a linear triatomic is given in Table 11B.1 on page 431, and if it is assumed that
the bond lengths are una�ected by isotopic substitution, the expressions for
the moment of inertia of the two isotopologues can be solved simultaneously
to obtain the two bond lengths.
�e rotational constant in wavenumber is given by [11B.7–432], B̃ = ħ/4πcI;
multiplication by the speed of light gives the rotational constant in frequency
units B = ħ/4πI, which rearranges to I = ħ/4πB
IOCS = (1.0546 × 10−34 J s)/[4π × (6081.5 × 106 Hz)] = 1.37... × 10−45 kgm2
IOCS′ = (1.0546 × 10−34 J s)/[4π × (5932.8 × 106 Hz)] = 1.41... × 10−45 kgm2
In these expressions the isotopologue with 32S is denoted S and that with 34S is
denoted S′. It is somewhat more convenient for the subsequent manipulations
to express the moments of inertia in units of the atomic mass constant mu and