Quick question: statistical mechanics

Therefore, the total number of distinct spin quantum states for the orthohydrogen molecule is 8. In summary, the orthohydrogen molecule has a total of 8 distinct spin quantum states, taking into account the electron spin states. This is determined by considering the fact that the molecule is composed of 4 distinguishable particles, each with 2 possible spin states, and the addition of electron spins to give the "orto" state. The calculation can be done using diagrams or combinatoric logic.
  • #1
Sojourner01
373
0
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.
 
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  • #2
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.
 
  • #3
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.
 
  • #4
Sojourner01 said:
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.
 

What is statistical mechanics?

Statistical mechanics is a branch of physics that uses statistical methods and probability theory to understand the behavior of large systems of particles, such as molecules or atoms. It aims to explain macroscopic properties of a system by analyzing the microscopic behavior of its individual components.

What are the basic principles of statistical mechanics?

The basic principles of statistical mechanics include the law of equipartition of energy, which states that all independent degrees of freedom of a system will have an equal share of the total energy, and the principle of microstate counting, which states that the most probable state of a system is the one with the highest number of microstates.

How is statistical mechanics related to thermodynamics?

Statistical mechanics and thermodynamics are closely related, as thermodynamic properties can be derived from statistical mechanics principles. Statistical mechanics explains the microscopic origins of thermodynamic behavior and provides a more detailed understanding of thermodynamic processes.

What are some applications of statistical mechanics?

Statistical mechanics has wide-ranging applications in physics, chemistry, and other fields. It is used to understand the properties of materials, such as phase transitions and the behavior of gases. It also plays a crucial role in the development of theories and models in fields such as astrophysics and biophysics.

What are some challenges in the field of statistical mechanics?

One of the main challenges in statistical mechanics is the complexity of systems with a large number of particles. Analytical solutions are often not possible, and numerical methods must be used to analyze the behavior of these systems. Additionally, statistical mechanics is an active area of research, with ongoing efforts to expand and improve upon existing theories and models.

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