# Rotational Energy

1. Dec 7, 2008

### roeb

1. The problem statement, all variables and given/known data
Calculate the internuclear distance R0 for the HCL molecule from the fact that some of the lines of its pure rotation spectrum occur at wavelengths: 120.3 um, 96.0 um, 80.4 um, 68.9um, 60.4um.
Assume 1H1 and 17Cl35
2. Relevant equations

$$E_{ROT} = \frac{ hbar^2 } {2I} l(l+1)$$
3. The attempt at a solution

I found the energy of each of the wavelengths:
E1 = 1.65 J
E2 = 2.07 J
E3 = 2.47 J
E4 = 2.89 J
E5 = 3.29 J
(that's really x 10^-21 for each)

Turns out that they are all .4 or .42 x 10^-21 Joules apart.
Why can they be .42/.4 joules apart? I was under the impression that a pure rotational spectrum would be like this: 0, 2Er0, 6Er0, 12Er0.

If I could figure this part out, I could easily calculate the moment of inertia and subsequently R0.