bei48482_FM

Molecules 285

Example 8.2

In CO the J 0 SJ1 absorption line occurs at a frequency of 1.15  1011 Hz. What is the

bond length of the CO molecule?

Solution

First we find the moment of inertia of this molecule from Eq. (8.11):

ICO (J1)1.46 10 ^46 kgm^2

In Example 8.1 we saw that the reduced mass of the CO molecule is m

1.14  10 ^26 kg.

From Eq. (8.5), Im R^2 , we obtain

RCO  1.13 10 ^10 m0.113 nm

This is the way in which the bond length for CO quoted earlier was determined.

8.7 VIBRATIONAL ENERGY LEVELS

A molecule may have many different modes of vibration

When sufficiently excited, a molecule can vibrate as well as rotate. Figure 8.18 shows

how the potential energy of a diatomic molecule varies with the internuclear distance

R. Near the minimum of this curve, which corresponds to the normal configuration of

the molecule, the shape of the curve is very nearly a parabola. In this region, then,

Parabolic approximation UU 0  k(RR 0 )^2 (8.12)

where R 0 is the equilibrium separation of the atoms.

1



2

1.46 10 ^46 kgm^2



1.14 10 ^26 kg

I



m

1.054 10 ^34 Js



(2)(1.15 1011 s^1 )



2 

J = 4

J = 3

J = 2

J = 1

J = 0

Rotational

energy

levels

Rotational

spectrum 

EJ

Figure 8.17Energy levels and spectrum of molecular rotation.

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