Estimating the energy required for dissociation from visible absorption spectra

I have been having trouble solving the following problem.
The question calls for an estimation of the energy (in kj/mol) required to dissociate ClO in its excited state when it is excited from the v = 0 of the ground state.


My first approach in solving this problem was selecting two transitions (v" = 2 to v' = 7 and v" = 3 to v' = 8).
I feel as though my error is in this part of the problem as the question asks for a transition from v = 0 but as far as I can see in the diagram there is no peak for the v = 0 transition.


Following this, I converted the wavelengths for each transition into wavenumbers and then subtracted the wavenumber corresponding to each transition:


$$\nu\_{7'0"} = \frac{10^7}{287\ \mathrm{nm}} \approx 34843.205\ \mathrm{cm}^{-1}$$


Then, subtracted $308\ \mathrm{nm}$ in wavenumbers from the above value to give $2375.68\ \mathrm{cm}^{-1}$ for the transition.


Then using the above numbers I used the following formula to find $\omega\_e$ and $\omega\_ex\_e$.


$$G\left(v'\right) = \left(v' + \frac{1}{2}\right)\omega\_e - \left(v' + \frac{1}{2}\right)^2 \omega\_e x\_e$$


Then with $\omega\_e$ and $\omega\_ex\_e$ I used the following formula to find the dissociation energy, $D\_e$,


$$D\_e = {\omega^2 \over 4\omega\_ex\_e}$$


Then subtracting the zero-point energy from $D\_e$ to get $D\_0$ and converting this value into kj/mol just to get an incorrect answer.
If anyone could point out where I'm going wrong that would be greatly appreciated.


[![Spectrum included in the question](https://i.stack.imgur.com/NTfwS.png)](https://i.stack.imgur.com/NTfwS.png)




Quiz 3 has been annoying.
From the graph, we know that the molecule dissociates at a wavelength of ~262.5 nm. We know this as this is when there are no more transitions, as indicated by the completely flat line.
Using the equation
E = (h \* c)/ν and substituting in the relevant values, we get E = 7.57E-19 J. Multiplying by Avogadro's number nets us ~456000 J/mol = 456 kJ/mol.


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