# RMS displacement of a diatomic atom

1. Apr 4, 2013

### Erubus

1. The problem statement, all variables and given/known data
A hypothetical atom is diatomic containing two identical atoms separated by an equilibrium distance. About this distance the atoms vibrate with the electric forces providing an effective spring constant of k = 4.0×10^−3 N/m. As the temperature of the sample is increased the amplitude of the vibration increases. At what temperature will the rms displacement of the atoms be x= 5.0×10−10m? (Answer: 72 K)

2. Relevant equations
<E> = 7kT/2

U = 7nRT/2

3. The attempt at a solution

I assumed that because of spring like nature of the atoms, this atom was a diatomic non rigid rotator, which is how I have those relevent equations. I am unsure if this initial assumption is even correct. Even if it was, I still don't have an idea of how to proceed from there.

2. Apr 5, 2013

### Staff: Mentor

It seems that you need to be modelling the bond as a harmonic oscillator. I imagine also that this should be considered as a classical oscillator, and not quantum mechanical. Then, you need to take out your classical mechanics textbook and figure out the relation between the energy of the oscillator and the amplitude of the oscillation, which will be related to the rms displacement $\sqrt{\langle x^2 \rangle}$.

3. Apr 6, 2013

### Erubus

Got it, thanks.