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**Another "where did the energy go" question**

I am struggling with a simple energy balance concept.

Two atoms, say Hydrogen, are traveling straight at each other with equal velocities.

This system has positive kinetic energy due to the motion of the atoms, but the momentum of the system is zero since the momentums of each atom cancel each other.

Now, the two atoms collide and (assuming the kinetic energy exceeds the bond energy) form a molecule of H2.

To conserve momentum, the velocity of the newly formed molecule must be zero, and so its kinetic energy must also be zero.

Some of the (prior) kinetic energy now exists as the bond energy of H2, but where is the rest?

If we were talking about two lumps of clay, we would say the extra energy had been converted to heat, but when we get down to individual atoms, that answer isn't satisfying.

I want to say that the extra energy is stored as kinetic/potential oscillation within the molecule, but I haven't been able to find a reliable source agreeing with that. Also, this would imply an upper bound on the amount of energy that could be stored in this fashion, but I don't see discussion of that in chemistry books.

I imagine my freshman chem prof explained this, but I can't remember and I can't find an explanation in a text.

Thanks for any clarity or pointers to references talking about this.