Vibrational frequencies of molecules

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Homework Help Overview

The discussion revolves around the vibrational frequencies of deuterium (D2) and hydrogen (H2) molecules, specifically comparing their frequencies given the mass difference and assuming the same spring constant for both. Participants explore the relationship between mass and vibrational frequency in the context of simple harmonic motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relevance of simple harmonic motion equations and the concept of reduced mass in relation to vibrational frequency. Questions arise about the necessity of specific values for spring constant and mass, as well as the implications of changing mass on frequency.

Discussion Status

The discussion is active, with participants providing insights into the nature of the problem and exploring different interpretations of the equations involved. Some guidance has been offered regarding the use of reduced mass in the context of two-body systems, but no consensus has been reached on the specific values needed for calculations.

Contextual Notes

Participants note the lack of certain information, such as the spring constant and the mass of a single atom, which may be relevant for solving the problem. There is also an acknowledgment of the complexity introduced by the two-body nature of the molecules involved.

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Homework Statement


The mass of the deuterium molecule D2 is twice that of the hydrogen molecule H2. If the vibrational frequency of H2 is 1.22 × 1014 Hz, what is the vibrational frequency of D2, assuming that the “spring constant” of attracting forces is the same for the two species?
Answer in units of Hz.


Homework Equations


Iowo=Ifwf
Io/f=(1/2)mr^2


The Attempt at a Solution



I want to use the above equation to solve this problem but I do not think that is the correct equation to use. There are too many variables that are not given in the question that I don't believe we are expected to know.
 
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It is vibration, not rotation...

How is related the vibration frequency to the mass? ehild
 
So it would be a simple harmonic motion problem?

v=(1/2*pi)(sqrt(k/m))?
 
Yes, the only difference is that we have two vibrating particles instead of one. This is a two-body problem, which can be treated as a simple harmonic oscillator with the same spring constant, but with a "reduced mass" instead of m. The reciprocal of the reduced mass is the sum of the reciprocal of the individual masses. We have two identical atoms now, so the reduced mass is just half of that of a single atom.

ehild
 
So for this problem I need to find out what the mass of a single atom is?
 
Do I even need to know the values for the spring constant and masses?
 
f=(1/2*pi)(sqrt(k/m)), so if m is doubled, what happens to f?
 

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