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2

... then (condense) the hydrogen into a liquid and then again used electrolysis. What would happen ? Nothing. You already separated the hydrogen and gave it's electron back to it. Hydrogen will not accept another electron (it's not stable).

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Assuming you could get down to liquid hydrogen and figure out how to do electrolysis at 33 K....it seems like the conductivity of molecular hydrogen would be quite low, and nothing would happen. Similar to the case of very pure water.

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These relations are based on the fact that both the position and the momentum distributions are centred around zero, which is in turn due to the symmetry of the atom. Given that, the width of the position and momentum distributions ($\Delta x$ and $\Delta p$) is of the same order as a typical position or momentum within those distributions ($r$ and $p$).

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The way this is justified is as follows: We start with the uncertainty principle, which can be roughly stated as $$\Delta x \Delta p \geq \hbar$$ For this rough estimate, we will ignore some factors of perhaps $2$ or $\pi$, but we're interested in some order of magnitude, not the exact result. Now, our second assumption will be that the ground state of the ...

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