PHYSICAL CHEMISTRY IN BRIEF

CHAP. 12: BASIC TERMS OF CHEMICAL PHYSICS [CONTENTS] 433

(12.28) forl→l−1 that the frequencies form a band with

ν=

h

4 π^2 I

l. (12.50)

Lines in the bands in rotational (and also rotation-vibration) spectra are thus separated by
∆ν=h/(4π^2 I).

Example

What is the distance between atoms in a^1 H^35 Cl molecule if the lines in rotation-vibration bands

are separated by 2060 m−^1?

Solution

From relation (12.50) it follows for the rotational moment

I=

h

4 π^2 ∆ν

=

h

4 π^2 c∆ ̃ν

=

6. 63 × 10 −^34 J s

4 × 3. 142 × 3 × 108 m s−^1 × 2060 m−^1

= 2. 72 × 10 −^47 kg m^2.

Since the reduced mass of the molecule is 1. 61 × 10 −^27 kg (see the example in section 12.2.4),

the interatomic distance is

r=

√

I

μ

=

√√

√√ 2. 72 × 10 −^47 kg m^2

1. 61 × 10 −^27 kg

= 1. 30 × 10 −^10 m= 0. 13 nm.

12.3.6 Raman spectra

Molecules may also interact with electromagnetic radiation in a way other than the photon
absorption or emission. A photon colliding with a molecule may be scattered. It means that
it changes its frequency (and therefore energy) as well as the direction of motion. A change in
the photon energy determines the change in energy of a molecule before and after the collision,

∆E=h∆ν. (12.51)