Question

What is the maximum wavelength a photon can have if it is to possess sufficient energy to cause this dissociation?

Answer 1

I attached the full question.
We need to calculate the enthalpy change first: 
$\Delta H= (247kJ)-(142.3kJ)=+105.2kJ$
Keep in mind this is the energy per mole, we need energy per atom:
$E=\frac{105200}{6.02 \cdot 10^{23}}$
We can see that this reaction needs the energy to get started (enthalpy change is positive).
The energy of a photon is given with this formula:
$E=\frac{hc}{\lambda}$
We need this photon to have the same energy (or higher) as our enthalpy change:
$105.2=\frac{6.62\cdot 10^{-34}\cdot 3\cdot 10^ 8}{\lambda}\\ \lambda=\frac{6.62\cdot 10^{-34}\cdot 3\cdot 10^ 8}{105.2/(6.02\cdot 10^{23})} \\\lambda=1.138\mu m$
This wavelenght is clasified as near infrared.