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Here's what I know about electrons.

Electrons have wave-like properties and the number of wavelengths in the $n^\text{th}$ shell is equal to $n(\lambda).$ Also, I read in my book that they have another property called spin.

But I couldn't imagine how a wave can have a property of spin. If this property is just a mathematical model, then is this property compatible for a wave i.e. Is it appropriate to use this property of spin with waves ?

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  • $\begingroup$ Note that this topic fits better to Physics SE site. $\endgroup$
    – Poutnik
    Commented Sep 15, 2020 at 9:10
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    $\begingroup$ I will probably never understand why it's often suggested that the questions about electrons are better suited for Physics.SE and at the same time the questions about dimensional analysis for some reason are perfectly fine for Chemistry.SE. $\endgroup$
    – andselisk ♦
    Commented Sep 15, 2020 at 9:17
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    $\begingroup$ In fact, spin is probably easier to define for a wave than for a particle. en.wikipedia.org/wiki/Angular_momentum_operator $\endgroup$
    – orthocresol
    Commented Sep 15, 2020 at 9:24
  • $\begingroup$ @andselisk I would it narrow down to some questions about electrons. Behaviour of electrons in context of atomic and molecular configuration is fine with me at CH SE. OTOH, nature of particle spin ? It is not so much about chemistry. It does not mean chemists cannot explain it. Some are surely familiar with spinors and Dirac equation ( not me ). About dimensional analysis, both physics and chemistry use many of shared and specific quantities, so it kind of belongs to both. $\endgroup$
    – Poutnik
    Commented Sep 15, 2020 at 9:25
  • $\begingroup$ @orthocresol As Dirac equation is a wave equation, I would think so. $\endgroup$
    – Poutnik
    Commented Sep 15, 2020 at 9:27

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An electron is not a wave nor a particle. An electron is usually described as a quantum object with some wave-like properties and some particle-like properties.

Some of them, like particularly a spin, do not have direct counterpart in our familiar macro world. It is a kind of a mysterious, specifically quantum property of all elementary particles and atomic kernels, that interact with angular momentum and interchange with it its values.

Non-relativistic quantum mechanics has no theoretical idea/model about the observed spin phenomena, that would come e.g. from resolving the Schrödinger wave equation. It was added just as an ad hoc extension. OTOH, the relativistic Dirac wave equation brings spin as the natural part of the quantum mechanical model.

Note that the classical idea about a spin as a rotation related angular momentum of a fast spinning small ball is wrong. Considering the electron mass, energy and the limit of the maximum electron size, an electron simply cannot rotate fast enough to have such amount of classical angular momentum, related to its eventual spinning.

Both orbital and spin contributions to the total angular momentum have their counterparts as orbital and spin magnetic momentum, if quantum objects have nonzero electric charge or charge nonhomogenity (like neutrons ).

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