A crystal contains $N$ atoms which possess spin $1$ and magnetic moment $\mu$. Placed in a uniform magnetic field $B$ the atoms can orient themselves in three directions: parallel, perpendicular, and antiparallel to the field. If the crystal is in thermal equilibrium at temperature $T$ find an expression for its mean magnetic moment $M$, assuming that only the interactions of the dipoles with the field $B$ need be considered.
I have 2 questions about this problem:
What does it mean for an atom to possess spin $1$ instead of $\pm \frac{1}{2}$? I thought particles can only have one of these 2 values for spin value.
How does a perpendicular orientation affect the probabilities of the other 2 orientations?In the book I am reading through, it gives an example with only a parallel and antiparallel possibility for spin. However, I know that intuitively these can't be the only 2 options. When the dipole flips from parallel to antiparallel, it must swing through a perpendicular state (assuming only $x,y$ directions apply here).
Best Answer
A atom is constituted of fermions(proton, neutron and electron). But whenever the atom an atom has even no of constituents it behaves like a boson. This is very easy to understand. All fermions have spin 1/2. So even no of fermions will have integer spin and therefor behave like bosons. Thus atom with spin 1 is possible.
Now given any value of spin S it will have (2S+1) eigenvalues s starting from -S to +S by steps of one. Remember these eigenvalues are discrete. And they give you the orientations. For your case the atom has spin 1. So it will have 3 eigenstates of spin. You named them to be parallel, antiparallel and perpendicular. But remember the spin is never completely parallel nor completely anti-parallel to the Magnetic field. There will always be some uncertainty.
You said:
But that's wrong. Because if the atom is spin-1/2, then there will only be two options namely the parallel and the anti-parallel one. There will not be any steps in between.