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Problem 3.9 Vibration of diatomic molecules
In previous analyses we’ve seen that the effective spring stiffness of the interatomic force is different for dif
ferent materials but doesn’t vary over a huge range. For concreteness, let’s take as a very rough estimate
k
s
= 10 N/m for these diatomic molecules.
(a) H
2
can be thought of as two simple springmass systems connected to the midpoint. Each simple system
has the mass of one hydrogen atom connected to a “spring” of half the full length of the interatomic “spring,”
and therefore with twice the stiffness (see Ex. 3.5 on page 83). So we can consider a simple springmass system
with a single atom and with a spring stiffness of 20 N/m. Note that
, since the frequency is
(1 cycle every
T
seconds).
Since we don’t actually know
k
s
for H
2
, it is also fine to estimate it as 10 N/m and ignore the halfspring issue.
In that case one gets
. The important result is that the frequency of vibration of a
diatomic molecule is of the order of 10
13
per second, a very high frequency indeed.
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This note was uploaded on 01/28/2012 for the course PY 205M taught by Professor Brown during the Spring '08 term at N.C. State.
 Spring '08
 Brown

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