# Rotational and vibrating energy levels - find energy separation

1. Aug 12, 2011

### bmarson123

1. The problem statement, all variables and given/known data
The equilibrium separation of the atoms in H35CI equals 1.27 x 10-10m. Calculate the energy separation between adjacent lines in the rotational-vibrational spectrum

2. Relevant equations

E = (n + 1/2)[STRIKE]h[/STRIKE]$\omega$ + [STRIKE]h[/STRIKE]2/ 2I * l(l+1)

I = $\mu$r02 $\mu$ = m1m2/ m1 + m2

3. The attempt at a solution

I am assuming the above equation for E is what I need to calculate to find the energy separation.

Using the above equation for inertia, I can find a value for it, meaning I can substitute it in.

I was wondering if it was possible for me to get rid of the n+1/2 and the l(l+1) parts from each bit if I assume n = 0 and l = 0?

$\omega$ is obviously the angular momentum, but if I want to calculate that I either need to know the frequency or the force constant, but to calculate either of these, I need the energy. So I'm very confused with what to do!

2. Aug 12, 2011

### ehild

Think of the selection rules and find the energy of the absorbed
photons. You can assume that all molecules are in the vibrational ground state but the rotational levels are filled even a room temperature, so there can be transitions 1→2, 2→3, 3→4, and so on.

ehild