In school, I've learned that we can only get an ortho hydrogen content upto 75%. Why is that we can obtain a pure sample of para hydrogen, but not ortho hydrogen? What prevents us from isolating ortho hydrogen?

  • $\begingroup$ Just how are you going to isolate it? $\endgroup$ May 10 '18 at 7:03
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    $\begingroup$ @IvanNeretin I couldn't imagine a method myself, but it seems weird to me that we are able to get 100% para hydrogen but not 100% ortho, when the only difference is in nuclear spin. Also the fact that the highest possible concentration we can obtain is 75%, why couldn't we go further than that? $\endgroup$
    – Favre
    May 11 '18 at 4:23
  • $\begingroup$ Should seem more weird that some separation can be done, when the only difference is in nuclear spin, which is awfully close to "no difference at all". In general, "why can't we" is almost never a question worth asking. Why can't we shoot an arrow into the Sun, really? $\endgroup$ May 11 '18 at 5:05
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    $\begingroup$ @IvanNeretin In general, 'why can't we?' is a question worth asking. These tend to be the most useful and fruitful for advancing one's intuition. (That's my humble opinion at least.) Your arrow-to-the-sun is an interesting mechanics question, quite advanced even once the whole picture is taken into account; I would probably upvote such a query if it showed some effort. $\endgroup$ May 12 '18 at 17:35

Ortho and para hydrogen differ in the alignment of their nuclear spins. The two hydrogen atoms each have a nuclear spin of 1/2 which results in a total nuclear spin of 0 or 1. The states with zero spin are called para and those with 1 ortho. The combination of the nuclear spins also results in the formation of a new spin wave function. There are 3 possibilities to get a nuclear spin of one with an even wave function and there is one possibilitie to get a spin of zero with an odd wave function. The overall wave function of the hydrogen molecule is given by the product of the electronic, vibrational, rotational and spin wave functions and should we antisymmetric with respect to exchange of the fermionic hydrogen nuclei. Because the electronic ground state of molecular hydrogen is even and the vibrational wave function of a diatomic molecule is always even, the wave function of para hydrogen has to be combined with the even rotational states and ortho with the odd rotational states. The absolute ground state of molecular hydrogen is thus the rotational state with zero rotation and is therefore para. The next state, with one quantum of rotation, is ortho.

You can only convert ortho and para hydrogen into each other using collisions or chemical reactions. To make pure para hydrogen, people use a catalyst at very low temperature. Because of the low temperature, all produced hydrogen will eventually end up in the absolute ground state, that is, para hydrogen. You cannot make ortho hydrogen this way because it does not represent the absolute ground state of the system. The 75% comes from the degeneracy of the Boltzmann factor: at low temperature (with no reaction catalyst) there are three times more ortho molecules with a spin of 1 than para molecules of zero spin.

Although you cannot make pure ortho hydrogen, you can study it by using narrow lasers that only excite odd rotational states.


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