bei48482_FM

286 Chapter Eight

The interatomic force that gives rise to this potential energy is given by differenti-

atingU:

Fk(RR 0 ) (8.13)

The force is just the restoring force that a stretched or compressed spring exerts—a

Hooke’s law force—and, as with a spring, a molecule suitably excited can undergo

simple harmonic oscillations.

Classically, the frequency of a vibrating body of mass mconnected to a spring of

force constant kis

 0  (8.14)

What we have in the case of a diatomic molecule is the somewhat different situation

of two bodies of masses m 1 and m 2 joined by a spring, as in Fig. 8.19. In the absence

k



m

1



2 

dU



dR

Parabolic approximation

U

U 0

R 0

R

Figure 8.18The potential energy of a diatomic molecule as a function of internuclear distance.

Force constant k

m 1

Force constant k

m (^2) = m′
m′ =mm, + , mm^22
Figure 8.19A two-body oscillator behaves like an ordinary harmonic oscillator with the same spring constant
but with the reduced mass m.
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