# Quick question: statistical mechanics

• Sojourner01

#### Sojourner01

Just a quick ponderance on a statistical mechanics problem.

"How many distinct spin quantum states has the orthohydrogen molecule?"

Does one include the electron spin states in the calculation? I'm inclined to say yes, as they most definitely have spin and most definitely are a different microstate for each arrangement. I'm not terribly familiar with the formulation of statistical mechanics so I'm not sure whether this is exactly what the question is asking, though.

Ortodydrogen molecule is a composite system made up by 4 particles. Each particle has 2 possible spin states. Using the fact that the electron spins are added as to give the "orto" state, compute all possible arrays of spin.

Excellent, that's what I thought.

So, taking the assumption that all particles are distinguishable - I presume this is standard for any quantum state question - there are 8 states of orthohydrogen by my counting. Correct?

I've drawn diagrams to work this out - the childish method. I just can't get my head around the combinatoric logic of working out microstates.

Excellent, that's what I thought.

So, taking the assumption that all particles are distinguishable - I presume this is standard for any quantum state question - there are 8 states of orthohydrogen by my counting. Correct?

I've drawn diagrams to work this out - the childish method. I just can't get my head around the combinatoric logic of working out microstates.

Two of the particles are identical, namely the electrons.