Vibrational frequencies of molecules

[Bearbull24.5]

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.

 

[ehild]

It is vibration, not rotation...

How is related the vibration frequency to the mass? ehild

 

[Bearbull24.5]

So it would be a simple harmonic motion problem?

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

 

[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

 

[Bearbull24.5]

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

 

[Bearbull24.5]

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

 

[ideasrule]

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