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CH3717 Statistical Mechanics > Section B > Flashcards

Flashcards in Section B Deck (19)
1
Q

The molecular partition function

A
• a sum of the boltzman factors of each energy level
• is a measure of the number of thermally active energy levels at said temperature (flats that are having parties)
• determines how particles distribute
• has a value independent upon the number of particles
• is a function per molecule
2
Q

The lowest level e

A

The loweste level, e, contributes E to the power 0 which equals 1, so contributes 1 to the sum

3
Q

The more accessilbe energy levels

A

the closer the contribution to the sum is to 1, thus partition function measures the number of thermally active enrgy levels.

4
Q

States share the same energy

A

They are degenerate (g)

5
Q

Translation

A

movement of molecule through 3D space

6
Q

Rotational partition function

A

energy levels that arise from rotation of the molecules about an axis

7
Q

Molecular rotation - symmetry

Homonuclear diatomics

A
• quantum mechanical properties of nuclei cause the occupation of only certain rotational states.
• given by sigma (2 for hetero, 1 for homo)
8
Q

Bosons

A

particles with integer spin

9
Q

fermions

A

particles with half integer spin

10
Q

anti-symmetry and symmetry

A

when two identicle particles are interchanged, the total wave function MUST change sign for FERMIONS and remain unchanged for bosons (OMG FERMIONS are so dramatic)

11
Q

Ortho and Para 1H2

A
• High temps dominating factor ortho has a nuclear spin degeneracy of 3. mixture 3:1 ortho:para
• low temps dominating factor is the lowest rotational state is only available to para. mixture is pure para
12
Q

Vibrational partition function

A

describes energy levels arising from vibrationn of molecules

13
Q

the harmonic oscillator

A

small displacements, stretching and compressing, obey Hooke’s law

14
Q

Electronic partition function

A
• This describes the consequence of energy levels available to be occupied by electrons in molecules.
• only a small number of electronic energy levels lie within a few kT of the ground state
• no way to caluclate the energy levels of a multi-electron atom/ molecule
• calculate the electronic partition function as an explicit sum of terms over electronic levels i:
15
Q

The electronic ground state

A

very often the electronic ground state lies much more thank kT below any excited state

16
Q

degeneracy of atomic electronic level

A

the degeneracy of an atomic electronic energy level can be found easily from its term symbol

17
Q

The overall molecular partition function

A
• for a closed shell molecule, the electronic degeneracy of the ground state is generally 1
• for a molecule like O2 with two electrons singly occupying degenerate orbitals, the electronic degeneracy is 3
• multiply the component partition functions together
18
Q

The overall molecular energy

A
• add the component energies together
19
Q

what does qtrans with large numbers mean

A

that there are many translational energy levels thermally available