BEISER MODERN PHYSICS Rotational Energy Level

[MARX]

Homework Statement

1. The rotational spectrum of HCl contains the following wavelengths:
   
   12.03 10 5 m 9.60 10 5 m 8.04 10 5 m 6.89 10 5 m 6.04 10 5 m
   
   If the isotopes involved are 1H and 35Cl, find the distance between the hydrogen and chlorine nuclei in an HCl molecule.

Homework Equations

E = J(J+1)h^2/(2I)[/B]

The Attempt at a Solution

I have the solution it says I have to use the difference in the frequency of above data
HERE IS MY QUESTION
why can't I apply the energy equation and use ONLY one of the wavelengths (E= hc/λ) to get the moment of inertia we know for longest λ above lowest energy hence J=0 There no
from there I know how to go from E to R using reduced mass
but that's not giving me the right answer [/B]

 

[DrClaude]

why can't I apply the energy equation and use ONLY one of the wavelengths (E= hc/λ) to get the moment of inertia we know for longest λ above lowest energy hence J=0 There no
from there I know how to go from E to R using reduced mass
but that's not giving me the right answer

What answer to you get?