Why doesn't the hydrogen spectrum show binding energies of 4.53 or 2.26 evolts?

[edguy99]

Just joined so I hope I'm in the right place:

My Question: I read that in the creation of a water molecules, a pair of hydrogen molecules break apart releasing 4.53 evolts of energy.
Why does the hydrogen spectrum show binding energies of -13.6, -3.4 ,-1.511, -.85, -.544 but not 4.53 or even 2.26 evolts?

 

[olgranpappy]

the water molecule is not a hydrogen atom. The water molecule's quantum mechanics is much more difficult to solve because it is a many body system whereas, effectively, the hydrogen atom is a single particle system. a hydrogen molecule, similarly, is not a hydrogen atom. a hydrogen molecule is also more difficult.

 

[edguy99]

Thanks for the reply. In a little more detail, I am trying to draw graphics to represent the bonding energies for Hydrogen and Hydrogen2 molecules and eventually build a water molecule.

To do this, I am connecting the most likely location of the electron(s) to the proton(s) and showing the energy of the photon produced if the bond is broken. The problem I have with this representation is when you break Hydrogen2 bonds, do you get 2.26 evolt photons and if so, why wouldn't this level of radiation show up in a hydrogen spectrum? Or does it?

I hope the little picture below helps show what I am trying to draw.