- #1
DanAbnormal
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I was wondering if anyone was familiar with what I am stuck on.
I understand the origins of ortho/para hydrogen, and how it is extended to the water molecule.
For 2 hydrogens:
If total nuclear spin = 0 -> Singlet state (para)
of total nuclear spin = 1 -> Triplet state (ortho)
This gives rise to the 3:1 ortho:para ratio for molecular hydrogen (and water) etc etc.
Now I am working with spectroscopy of water, and I have quantum numbers describing energy states. The numbers are:
J,Ka,Kc,v1,v2,v3
The J,Ka,Kc numbers being the standard asymmetric top q-numbers describing rotation.
J= total ang. mom.
and Ka, Kc the projections on the A and C axes, respectively.
the v1,v2,v3 numbers correspond to symmetric stretch, symmetric bend and asymmetric stretch vibration modes, respectively.
THE QUESTION: I have read in countless papers (without explanation) that ortho and para states can be distinguished like so:
If Mod(Ka+Kc+v3,2)=0 -> para
or if =1 -> ortho
Or equivalently, if Ka+Kc+v3 is even -> para
or if odd -> ortho
I don't understand why this is so. Can someone explain the physics behind this, I really don't get it... Am I missing something?
Thanks
Dan
I understand the origins of ortho/para hydrogen, and how it is extended to the water molecule.
For 2 hydrogens:
If total nuclear spin = 0 -> Singlet state (para)
of total nuclear spin = 1 -> Triplet state (ortho)
This gives rise to the 3:1 ortho:para ratio for molecular hydrogen (and water) etc etc.
Now I am working with spectroscopy of water, and I have quantum numbers describing energy states. The numbers are:
J,Ka,Kc,v1,v2,v3
The J,Ka,Kc numbers being the standard asymmetric top q-numbers describing rotation.
J= total ang. mom.
and Ka, Kc the projections on the A and C axes, respectively.
the v1,v2,v3 numbers correspond to symmetric stretch, symmetric bend and asymmetric stretch vibration modes, respectively.
THE QUESTION: I have read in countless papers (without explanation) that ortho and para states can be distinguished like so:
If Mod(Ka+Kc+v3,2)=0 -> para
or if =1 -> ortho
Or equivalently, if Ka+Kc+v3 is even -> para
or if odd -> ortho
I don't understand why this is so. Can someone explain the physics behind this, I really don't get it... Am I missing something?
Thanks
Dan