- #1

Wledig

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- Thread starter Wledig
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- #1

Wledig

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- #2

Henryk

Gold Member

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It might be a bit easier to understand a much simpler system, say only three particle, each one can have energy of 1,2,3,4,5,6 J (like dice).

If the particles are classical, there are the following states with the total energy of 7 J (using the notation (x,y,z) where x, y, z, are, respectively, energies of the first, second and third particle):

(1,1,5), (1,5,1), (5,1,1), (2,2,3), (2,3,2), (3,2,2), (1,3,3), (3,1,3), (3,3,1), (1,2,4), (1,4,2), (2,1,4), (2,4,1), (4,1,2), (4,2,1)

Therefore, we have 15 possible states of the three particle system and each of them gives us a total energy of 7 J.

This is the case when the particles are distinguishable. If these are idential quantum particles, they are not distinguishable. That means that the state with two particles of energy 1 J and the third with energy of 5 J is the same as the state with the first particle of energy 5 J and the remaining 2 of energy of 1 J ( you can't tell which is the first and which is the third particle!).

So, in quantum statistics, there are only the following states:

(1,1,5), (2,2,3), (1,3,3), (1,2,4), only 4 states.

- #3

Wledig

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- #4

crossword.bob

- 11

- 4

- Three degrees of freedom from translational velocity of its centre of mass,
- Two degrees of freedom from rotational frequency about axes perpendicular to the molecule's primary axis,
- One degree of freedom from vibrations between the two atoms.

Each degree of freedom can accept certain quanta of energy; the number of states is the total number of ways you can assign these quanta to individual components.

- #5

Wledig

- 69

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I see, thanks for confirming that.

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