Wikipedia:Reference desk/Archives/Science/2023 August 11

= August 11 =

Magnetic moment
Why does this table seem to make no sense? Neutron magnetic moment almost as strong as proton instead of 0 (signed same as electron), alpha particle exactly 0 even though it's charged, it seems like the electron-currentless bare nuclei should all be the sum of their parts but they aren't, (unsigned) proton:electron moment ratio isn't even near their mass ratio (at least the moment signs aren't the same)... Sagittarian Milky Way (talk) 14:48, 11 August 2023 (UTC)
 * You can't treat elementary particles like hard little balls that behave in ways your intuition, in dealing with objects in your everyday life, thinks they should. Don't project what you know from classical physics on elementary particles.  It never works, and you'll just confuse things.  First of all, your confusing the Classical electromagnetism of magnetism with what is going on with fundamental particles.  The classical understanding, that moving electric charge generates a magnetic field, works for things like maxwell's equations and building electromagnets and dynamos and the like.  Protons and quarks and electrons don't behave like that.  These particles have what is called an intrinsic magnetic moment, which like quantum spin, is not a property of the particle because it has movement.  Quantum spin is not due to the particle actually turning around an axis, rather it is an intrinsic bit of angular momentum that the particle just has.  Similarly, intrinsic magnetic moment is not due to any sort of motion or rotation or anything the particles are physically doing, it just is.  Secondly, the way that protons and neutrons are built of quarks, and similarly the way that protons and neutrons get together to form nucleii, is not intuitive in a physical sense.  They don't just glom onto each other like you see in pictures like this to the right.  Nuclear structure will give you some idea of the complexity of the situation.  My point is, don't have expectations when looking at data like you're complaining about.  Your intuition for how things "should" behave, based on the facile understanding of elementary particles as though they obeyed the intuitions you have from classical physics, is just wrong.  It's always going to be wrong.  Don't try to apply it.  It always leads to wrong conclusions and confusion.  -- Jayron 32 15:30, 11 August 2023 (UTC)
 * No I'm not confusing charge motion-induced magnetism with intrinsic electromagnetism, was just mentioning that at least the nuclei listed are bare so these moments are spared the extra complications of the motion of electrons (some electrons are even close enough to c to significantly affect the element, but to know the speed means the location's a probability cloud that doesn't move so is the "orbiting current" still affecting the magnetic dipole moment?). So I guess the neutron up quark will tend to orient a certain way in a magnetic field? Will they curve in a field despite being neutral? Do lasers curve? Is most of the magnetar magnetism from neutrons? Why are Fe-Ni significantly more magnetizable than most things i.e. polar H2O molecules? You have to really blast unusually small frogs to levitate them. Why does that not fuck the frog more? They don't even get tazed or seizured from induced currents. Do the quantum levels of Fe-Ni or the 2 electrons per level opposite spin thing play a role? Sagittarian Milky Way (talk) 19:35, 11 August 2023 (UTC)
 * Why does neutron have a magnetic moment you ask? If you are not surprised that a electromagnetic coil (supposedly electrically neutral) with a current in it has one, than you should not be surprised by the magnetic moment of neutron. As to the alpha particle and why it does not have a magnetic moment? Here you should note that the magnetic moment is a vector and therefore it has a direction. But, for any quantum particle the only (pseudo)vector that is associated with it is its spin. So, the magnetic moment must be always proportional to the spin. However the spin of alpha particle is zero, so must be its magnetic moment. Ruslik_ Zero 20:14, 11 August 2023 (UTC)
 * That's interesting, quantum particles only have one vectoroid thing. So quantum mechanics is not always a near-infinite reservoir of complexity. So why do the spins cancel out? Since there's no negative spins on that table it can't be additive and for a moment I thought it might be modulo 1 but then I saw a deuteron has a spin of 1 and 2 deuterons fused together has a spin of 0. What's the difference between a spin of 1 and 1/2? Sagittarian Milky Way (talk) 20:43, 11 August 2023 (UTC)
 * The spins in that table are scalar rather than vector. They don't include directionality since it wouldn't make sense to do so. Take an electron; it always has a scalar spin magnitude of 1/2, but the direction making it a vector quantity can either be "up" (positive) or "down" (negative). Which direction it takes, outside of other interactions, is essentially irrelevant, since both would have the same energy (they are degenerate). However, for an electron within an orbital, it does matter, due to the Pauli exclusion principle. So, let's look at a 1s atomic orbital. If it is "empty," then it has a spin of 0 because nothing is in it. If it has one electron, then the spin is either -1/2 or +1/2 (and it doesn't really matter which, because energetically they are identical or degenerate). However, if we have two electrons in the orbital, then one of them has to be -1/2 and the other has to be +1/2, as otherwise both electrons would have the same quantum state, which is forbidden. The sum of -1/2 and +1/2 is obviously 0, so a helium atom would have a magnetic moment of 0. If we look at an Fe3+ ion, all of the orbitals are doubly occupied except for the 3d orbital electrons, the 5 orbitals each being singly occupied (5 electrons in 5 orbitals). The energies in this example favor all of these 5 electrons having the same spin, either all spin "up" (+1/2) or spin down (-1/2). This doesn't violate Pauli exclusion since, while the principle quantum numbers are the same (3) and the azimuthal quantum numbers are the same (2) and the spin numbers are the same (-1/2 or +1/2, but all being the same), the orbital magnetic numbers are all different (-2, -1, 0, 1, 2). As a result, the Fe3+ ion has a non-zero magnetic moment. As for why those spin numbers are 1/2 instead of 1, these are dimensionless quantities that we literally defined as such (1/2). There's no reason we couldn't have written them as 1 instead of 1/2, but then we would have to change other numbers as well to match that change. It's arbitrary as long as they all relate to each other correctly, so by convention, we do 1/2. --OuroborosCobra (talk) 22:39, 11 August 2023 (UTC)
 * Oh, I should note than in my Fe3+ example, I'm illustrating a high spin scenario. It is possible to have other arrangements that do not violate Pauli Exclusion, such as a low spin form where 2 of the 3d orbitals are doubly occupied and only 1 orbital is singly occupied. The result would be an ion that had a much smaller magnetic moment than the high spin form, but still has a non-zero magnetic moment. As to why an ion is high spin or low spin or intermediate spin, that gets into a whole other topic of things like ligand field theory, d-orbital splitting, pairing energy, and other topics generally contained within the field of inorganic chemistry. --OuroborosCobra (talk) 22:48, 11 August 2023 (UTC)
 * Does nucleon magnetic moment help? fiveby(zero) 20:20, 11 August 2023 (UTC)
 * Yes. Sagittarian Milky Way (talk) 21:07, 11 August 2023 (UTC)