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I know that the s-orbitals of H atom are spherically symmetrical. But the p,d or f orbitals aren't. So, the H-atom needn't necessarily be spherically symmetrical, as the wave-function would be a linear combination of all the orbitals. But, in a certain hypothesis, if I assume the H-atom to be spherically symmetrical, what could I possibly comment on the specific orientations of $p_{x}$, $p_{y}$ and $p_{z}$ orbitals in space? The radial and angular wave-functions might/mightn't change for the p-orbitals, but how to comment on their spatial orientations? Can someone help me out in this?

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  • $\begingroup$ Why take care of the $p$ orbitals of the hydrogen atoms ? It is like its $d$ and $f$ orbitals. They are empty. So why discuss about their spatial orientation and of their linear combinations ? $\endgroup$ – Maurice Feb 2 at 20:48
  • $\begingroup$ Okay, but what about the excited states? Is it unnecessary altogether to look at $p$ or $d$ orbitals, or even $f$ orbitals in H atom? $\endgroup$ – Abhinav Tahlani Feb 17 at 6:28
  • $\begingroup$ Why take care of the excited states of the H atom in chemistry ? They last less than a nanosecond. $\endgroup$ – Maurice Feb 17 at 9:05
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In "real life", the hydrogen atom has its only electron in the s orbital. And unless it gets to an excitated state, that's the only thing that matters (whether you're studying the energy of the atom or the bounds it can make in terms of energy or symmetry). Nevertheless, the H atom is likely to have a spherical symmetry, so any of its p-orbitals will be orthogonal to the others, so their linear combination is likely to keep the overall spherical(-ish) symmetry of the atom. Here is a representation of such orbitals :

[Conventional representation]

(Reference)

Hope this helps!

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