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Electrons and protons are spin-$\frac{1}{2}$ particles, so under a rotation by 360$^\circ$, their wavefunction changes by a sign. They are also commonly found alone in chemical reactions, especially protons (H$^+$ ions). Does this 720$^\circ$ rotation-invariance property have any important effects on chemistry?

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I almost voted to close your question as a duplicate of How do you rotate spin of an electron?. This would be controversial because the question looks related at a first glance, but ACuriousMind's answer to that question also (indirectly) answers this question.

When we talk about rotating an electron, or any fermion, we are not talking about a physical rotation in the sense of rotating any macroscopic body. ACuriousMind explains this very clearly here. So the rotational properties of the fermion wavefunction have no direct physical relevance to chemistry. If you rotate an electron by $2\pi$ it's still the same electron.

For completeness I should make the obvious comment that the fact electrons are fermions means they obey Fermi-Dirac statistics and this underlies all of chemistry. So in this sense the rotational behaviour is intimately related to chemistry. However I assume you're asking specifically about rotation and not about the effect of the electron being a fermion.

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In quantum physics and quantum chemistry , spin isnt an actual rotation of a particle , it is just a quantum property of a particle.

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  • $\begingroup$ Electron spin is angular momentum in every sense. $\endgroup$ – my2cts Apr 26 '19 at 19:07
  • $\begingroup$ No it isnt . It is a quantum property of a particle. $\endgroup$ – Donald Duck Apr 27 '19 at 8:11

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