What is the probability the bonds broken with sunlight reforming back?

Question

The maximum wavelength $\lambda$ capable of breaking a chemical bond can be estimated as $\lambda = hc/E.$ UV-A $(\pu{380 nm})$ can break bonds with the energy up to $\pu{315 kJ mol^-1},$ UV-B $(\pu{320 nm})$ can break $\pu{374 kJ mol^-1}$ bonds, etc.

So, the sunlight (at UV) can break both the $\ce{C-C}$ and the $\ce{C-O}$ bonds. Sunlight has enough energy to break up vitamin C molecules in juice. Supposedly plants have some excision repair. But on the chemistry side, when UV breaks a bond, what's the probability the bond can just reform back?

I'm going to assume there are multiple factors. What are factors where 50% of the time, the bond can just reform, as well as factors where ~90% and ~10% of the time, the broken bond can just reform back?

Answer 1

UV light creates an excited electronic state, on this electronic state the nuclei are no longer in an equilibrium position and begin to move, i.e. start to move towards breaking the bond. This is the simple semi-classical picture where we view nuclei as classical point particles. More correctly we should speak about the dynamics of the nuclear wavefunction on the excited electronic state potential. But the idea is the same. The initial nuclear wavefunction is no eigenfunction of the excited electronic state and thus "moves".

It is very difficult to describe the dynamics of this process as it involves nuclei and electrons at the same time. A bond can be broken if the wavepacket moves along a vibrational coordinate, elongating the bond. Another aspect that is the exchange of energy between electrons and nuclei. At some point the electronis typically relax via internal conversion to the electronic ground state. Energy is conserved during this step and the decrease of potential energy of the electrons is transferred to the nuclei as kinetic energy.

This excess energy can lead to bond breaking in the groundstate, since the nuclei are now in an excited vibrational state that may lie across a potential barrier that kept the initial bond stable.

This answer is also useful if you want to get a better understanding how bonds are broken.

Lastly we also need to consider exchange of energy with the environment, which allows the molecule to cool down by exchanging vibrational energy with other molecules. This will make the whole process irreversible and stop the dynamics eventually.

The question for a simple probability to reform a bond is thus very difficult and has no simple universal answer. You need to look at all the steps that I have described, which dependent on the molecule in question and the conditions, to work out an answer. You may be able to measure these processes but then again it will depend on the molecule and the conditions and there is no universal answer.