Homework Help: What is particle spin?

Re: spin

In a word, yes - it is an intrinsic property of particles. It is often thought about as the quantum of angular momentum, since it has such units, but it is not correct to think of it as the result of spinning motion of a rigid object. It really is a fundamental property elementary particles. Electrons and quarks, for example, have spin 1/2, and that cannot ever change.

Particles can be in different "orbital angular momentum" states, however, as in the different orbital levels of electrons bound to atoms. To calculate all their electromagnetic interactions in detail, however, you have to consider both their orbital and their spin angular momentum.

 

Re: spin

Sorry, I don't know anything about molecular dynamics, but I would guess that if molecules are free to develop angular momentum states, e.g. if they are free and not bound in some kind of lattice, then those states would be quantized like any other. In other words, I would expect molecules to take on discreet (quantized) values.

The numbers you give for the u/d quarks are their electric charge values (measured in the same units in which the electron has a charge of -1, but never +1). Electric charge is conserved and cannot change the way a spin state can change.

These are different kinds of states, however. The electron spins states are defined relative to the axes of our regular spatial coordinates, which have no preferred directions, so electrons are free to spin in any direction. (An applied magnetic field can break the directional symmetry, so you then get preferred states, i.e. the spin states will align with the field.)

The spins that define strongly interacting particles is called isospin and is really defined in a different abstract mathematical space, i.e. it's not the position space we live in. This is related to the different quantum numbers taken by the different quarks, including their electric charge values, but it's important not to confuse isospin with the "normal" spin defined relative to the usual x,y,z axes.

Lastly, the Pauli Exclusion Principle applies to ordinary spin, e.g. the 1/2 spin of electrons. Quarks also have spin 1/2, however (normal spin, not isospin), so they also obey the exclusion principle, as do all particles with 1/2 integer spin (i.e. Fermions). Particles with integer spin (Bosons) obey Bose-Einstein statistics and are not bound by the exclusion principle.

 

Re: spin

Well, as said, the Pauli principle applies only to spin. But anyway, on the topic of the spin of molecules:

If you know some basic chemistry, you'll know that the vast majority of the time, molecules have an even number of electrons - all electrons are paired. In this case, the molecule doesn't have spin, as the pairs consist of one spin-up electron and one spin-down electron, combining into a total of zero spin - known as a singlet state. The next spin state would be a triplet state, with two unpaired spins. This is usually significantly higher in energy and wouldn't need consideration.

If the molecule has an odd number of electrons, it's termed a radical, and has a doublet as its lowest spin state (one unpaired spin). Radicals generally have a fairly high energy due to this, which is why they've got a reputation for being quite reactive.

The other situation where you end up having to take spin into consideration in chemistry is with transition-metal complexes. Since a transition-metal ion has a relatively large number of d-orbital energy levels that are fairly close in energy, and the relative energy of these orbitals depends very much on the ligands. So, in transition-metal complexes a 'higher' spin state may be lower in energy or at least low enough in energy to result in mixed spin state.

So in short, when studying these kinds of reactions, you need to take into account different spin states. Rather than describing the reaction as proceeding on a single potential-energy surface (energy in terms of nuclear coordinates), you have to take into account that there are other potential-energy surfaces (for other spin states), and the fact that you may have transitions between these surfaces during the reaction at the points where they intersect each other.

Most chemists don't work with radical or transition-metal reactions, so they don't need to think about spin much. In other words, the triplet and other 'higher' spin state potential-energy surfaces remain significantly higher in energy in the reactant, product and intermediate states (no crossings), and don't need to be taken into account.

 

Re: spin

Depends on what you mean.
If you mean 'What effect does spin have on a molecule of nonzero total spin?' then the answer is: Relatively little. A molecule with a total overall spin will often be a radical, making it quite reactive. Spin explains why electrons tend to form pairs.

If you mean: 'What effect does electronic spin have on the formation of molecules?' then the answer is: Enormous. If electrons had no spin, or an integer spin, they would be bosons and not bound by the Pauli Exclusion Principle. You would no longer be limited to two electrons in an orbital, and most electrons would simply stay in the lowest, s, orbital. The periodic table would not exist. Chemistry would be entirely different.