# Homework Help: Vibrational frequencies of molecules

1. Apr 18, 2010

### Bearbull24.5

1. The problem statement, all variables and given/known data
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?

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

3. 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.

2. Apr 18, 2010

### ehild

It is vibration, not rotation...

How is related the vibration frequency to the mass?

ehild

3. Apr 18, 2010

### Bearbull24.5

So it would be a simple harmonic motion problem?

v=(1/2*pi)(sqrt(k/m))?

4. Apr 18, 2010

### ehild

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

5. Apr 25, 2010

### Bearbull24.5

So for this problem I need to find out what the mass of a single atom is?

6. Apr 25, 2010

### Bearbull24.5

Do I even need to know the values for the spring constant and masses?

7. Apr 25, 2010

### ideasrule

f=(1/2*pi)(sqrt(k/m)), so if m is doubled, what happens to f?