Section B

Question 1

The molecular partition function

Answer 1

• 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

Question 2

The lowest level e

Answer 2

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

Question 3

The more accessilbe energy levels

Answer 3

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

Question 4

States share the same energy

Answer 4

They are degenerate (g)

Question 5

Translation

Answer 5

movement of molecule through 3D space

Question 6

Rotational partition function

Answer 6

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

Question 7

Molecular rotation - symmetry

Homonuclear diatomics

Answer 7

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

Question 8

Bosons

Answer 8

particles with integer spin

Question 9

fermions

Answer 9

particles with half integer spin

Question 10

anti-symmetry and symmetry

Answer 10

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)

Question 11

Ortho and Para 1H2

Answer 11

• 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

Question 12

Vibrational partition function

Answer 12

describes energy levels arising from vibrationn of molecules

Question 13

the harmonic oscillator

Answer 13

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

Question 14

Electronic partition function

Answer 14

• 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:

Question 15

The electronic ground state

Answer 15

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

Question 16

degeneracy of atomic electronic level

Answer 16

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

Question 17

The overall molecular partition function

Answer 17

• 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

Question 18

The overall molecular energy

Answer 18

• add the component energies together

Question 19

what does qtrans with large numbers mean

Answer 19

that there are many translational energy levels thermally available