Question: In QM and assuming you could repeat the same exact bond-breaking experiment arbitrary number of times, do bonds always break at the same stretch length, or does the uncertainty principle require some variability in the stretch length at which the atoms debond?

Answer: 
A direct answer to this question is not simple. The main difficulty is related to the formal definition of what a chemical bond is. 

The most useful definitions of bond in the case of molecules and condensed matter either rely on the introduction of molecular orbitals, analyzing the role played by orbitals and their energy on the cohesive property of the system, or are based on a careful analysis of the topological properties of the electronic charge density (this is the modern approach of "*atoms in molecules*" proposed by [Bader and coworkers](https://onlinelibrary.wiley.com/doi/pdf/10.1002/jcc.20528) a couple of decades ago.

At the best of my knowledge, all the attempts to put on a more formal base the concept of chemical bond hinge on electronic density or electronic wavefunctions, which means that the concept of bonding, bond formation, bond stretching or bond breaking, are all based on quantities which already embody in their definition some average statistical behavior. Electron density is an average quantity. An orbital allows to evaluate its associated probability density and therefore averages and uncertainties (standard deviations). Therefore, every statement about bonds is based on **properties of the whole statistical ensemble** underlying the statistical interpretation of quantum mechanics.

On the basis of these considerations, my answer is that **bonds always break at the same stretch length** due to the existing definitions of bond.
The way quantum mechanics sees molecular bonding is the existence of a bound state (By the states I mean the energy eigenstates for the electrons in the potential provided by the protons ) which has energy lesser than the bound states in the constituent atoms. The potential between two atoms is usually modelled using morse-potential or morse-potential like potentials. [![enter image description here](https://i.stack.imgur.com/szgSf.png)](https://i.stack.imgur.com/szgSf.png)

This model tells us that if we excite the electron to a higher energy state it becomes more and more delocalised because the wave function is more spread out.

[![enter image description here](https://i.stack.imgur.com/8MIjn.png)](https://i.stack.imgur.com/8MIjn.png)

Now, this is how we explain the electron having a high probability of leaving the molecule and ionising it. Now, let's try to turn this idea on its head. 

**\*I am taking a bit of freedom here, would be happy to receive feedback from the peer \***

Now if we look at the Morse potential and think that the atomic nucleus is slowly moving away from each other (so slow that it is almost stationary for the electron). Then we can see that we are automatically pushing our electron to a higher more and more delocalised wavefunction for this potential. So now the electron is moving around a lot more. 

But as we move the atoms away from each other the potential of individual atom starts coming into play. 

[![Individual Atom potential](https://i.stack.imgur.com/F8sxQ.gif)](https://i.stack.imgur.com/F8sxQ.gif)

Now the moment the potential well for an individual atom is deeper than the potential well for morse potential, the electron will then move to the individual atoms leaving the molecular state. This is how I think bonds are broken. 

Now, in this picture, I think bond breaking is not a discrete event because at some point during this transition the morse potential and the atomic potential would be comparable and there will be an asymmetric potential well with the electron tunnelling between the two wells. And hence we indeed will have an uncertainty in the bond breaking length but I am not sure it is in any way analogous to the uncertainity principle. It is more like a transition state with a finite probability of both molecular and atomic state existence.

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Follow up: Too long for comment

Hi SuchDoge, I am sorry, I do not see a solution to this problem. Firstly, because the Morse potential I have mentioned is an assumption which breaks down at higher energy levels. And as far as I know, most potential which are entered by hand do break down at higher energy levels. Most research I tried to look for focus on energy states in the molecular form, many did mention decay into an atomic form but gave no explanation for that. And about the order of magnitude estimate, I think there is definitely no such general estimate that uniquely emerges from quantum mechanics. I think if one goes down the road of too simple upper and lower bounds then even normal electrodynamics and maybe even simple geometry may give you some bounds.