# determine at which v and J the rotational and vibrational energy differences are equal

I was presented with this question and I started working on it but I ran into a problem.
We've got $\Delta E_{rot} = 2B_e(J+1)$ and $\Delta E_{vib} = \hbar \omega$

We get to the point that we've got $J= \hbar\omega/(2B_e)-1$ but we know that J should be a lot larger than 1 so we don't quite know what we've done wrong. Can anyone help us?

We are given that $\omega _e =4400$ and $B_e = 60.9$

• What are the units of $\omega_e$ and $B_e$? I assume they are given in cm$^{-1}$. If so, your formulas (in J) should read $\Delta E_\text{rot}=2hcB_e(J+1)$ and $\Delta E_\text{vib}=hc\omega_e$. – Paul Sep 5 '16 at 11:54
• Aah, We missed the speed of light in the vibrational energy. We had hc in the rotational energy formula but removed it. Thanks. – Arno van der Weijden Sep 5 '16 at 13:49