What is the quantum spin of a single electron in an (atomic) orbital?

In summary, the quantum spin of the valence electron in the silver atom in the furnace in the Stern-Gerlach experiment is unpredictable and can be described using a density matrix. It is not affected by the lack of a magnetic field in the furnace. The second electron in an orbital always has the opposite spin of the first electron in the same orbital, but the appropriateness of the orbital picture itself is debated.
  • #1
Curious Cat
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0
TL;DR Summary
I wrote a little (computer) program to fill in the atomic electron
configuration one electron at a time, for children, and it got me
thinking, about this.
What is the quantum spin of the valence electron in the silver atom in
the furnace in the Stern-Gerlach experiment?
. Up, down, at random, alternating, in a (quantum) superposition (of
both), or none? Does it even have/get one until it's measured/observed
/needed?
. Does the second electron, in an orbital, have to have the opposite
spin to start, with, or is it made to conform?
 
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  • #2
In the furnace, the quantum spin of the valence electron of the silver atom should be random, no? There is no magnetic field inside the furnace relative to which there would be any reason that it should be up, or down.
(This can be described by using a density matrix instead of a wave function. One reason for using that description is that it makes it clear that there is no difference whether you assume that one half is up and the other half down, or that one half is left and the other half right, or that a quarter is respectively up, down, left, and right, or that the state is basically just totally random. ... But that goes into territory where only very patient children would be able to follow.)

The second electron in an orbital has the opposite spin of the first electron in the same orbital, otherwise it would be wrong to claim that both electrons are in the same orbital. Whether the orbital picture itself is fully appropriate is a separate question.
(Advanced level explanation: the orbitals which arise from the Hartree-Fock approximation cannot be fully appropriate. However, orbitals also arise from density functional theory computations, and there it is less clear whether they are appropriate or not, even so their exact interpretation remains unclear.)
 
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Related to What is the quantum spin of a single electron in an (atomic) orbital?

What is quantum spin?

Quantum spin is an intrinsic property of particles, such as electrons, that determines their angular momentum and magnetic moment. It is not the same as the physical spinning of an object, but rather a fundamental property of particles that cannot be explained by classical physics.

What is the quantum spin of an electron?

The quantum spin of an electron is always equal to 1/2, which is a fundamental constant in physics. This means that the electron's spin can only have two possible values: +1/2 or -1/2.

What is an atomic orbital?

An atomic orbital is a mathematical function that describes the probability of finding an electron in a specific location around an atom's nucleus. It is used to represent the electron's energy and spatial distribution within an atom.

How does the quantum spin of an electron affect its behavior in an atomic orbital?

The quantum spin of an electron is one of the quantum numbers that determines the electron's energy and behavior in an atomic orbital. It affects the electron's magnetic properties, as well as its interactions with other particles and electromagnetic fields.

Why is understanding the quantum spin of a single electron important?

Understanding the quantum spin of a single electron is crucial for understanding the behavior of matter at the atomic and subatomic level. It also has practical applications in fields such as quantum computing and magnetic resonance imaging (MRI).

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