Ch4 HW6 Solution

Ch4 HW6 Solution - Problem 3.9 Vibration of diatomic...

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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 spring-mass 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 spring-mass 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 half-spring 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.

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