PHYSICAL CHEMISTRY IN BRIEF

CHAP. 12: BASIC TERMS OF CHEMICAL PHYSICS [CONTENTS] 423

12.2.4 Rotation

Rotation is another type of molecular motion. The simplest model of a molecule is arigid
rotor, i.e. a pair of atoms at a fixed distancer. Its energy is given by the relation

Vrot=

1

2

Iω^2 , (12.25)

whereωis the angular velocity and
I=μ r^2 , (12.26)

is themoment of inertia. It is expressed using thereduced mass

μ=

m 1 m 2

m 1 +m 2

, (12.27)

wherem 1 andm 2 are the masses of the atoms.

Example

Calculate the reduced mass of the molecule^1 H^35 Cl.

Solution

The mass of an atom is calculated as the ratio of the atomic mass and the Avogadro constant

[see1.5.2]

mH=

1 g mol−^1

6. 022 × 1023 mol−^1

= 1. 66 × 10 −^24 g,

mCl=

35 g mol−^1

6. 022 × 1023 mol−^1

= 5. 18 × 10 −^23 g.

The reduced mass is thus

μ=

1. 66 × 10 −^24 g× 5. 18 × 10 −^23 g

1. 66 × 10 −^24 g+ 5. 18 × 10 −^23 g

= 1. 61 × 10 −^24 g,

i.e. slightly lower than the hydrogen atom mass.

The energy eigenvalues are

Erot=

h^2

8 π^2 I

l(l+ 1), (12.28)