Transcript Molecule B(MHz) σ q Rot

ROTATIONAL PARTITION FUNCTIONS:
We will consider linear molecules only.
Usually qRotational » qVibrational . This is because:
1. rotational energy level spacings are very
small compared to vibrational spacings and
2. each rotational level has a 2J+1 fold
degeneracy. Due to degeneracy the
populations of higher J levels are much
higher than would be otherwise expected.
ROTATIONAL PARTITION FUNCTIONS

ROTATIONAL PARTITION FUNCTIONS:

ROTATIONAL PARTITION FUNCTIONS:

ROTATIONAL PARTITION FUNCTIONS:
The last formula is “valid” (i.e. a good
approximation) for almost all unsymmetrical
linear molecules. Aside: For symmetrical
linear molecules rotational levels may not all
be populated. Only half are populated for
16O (all are populated for 16O18O!). We need
2
a symmetry number, σ, equal to 1 normally,
or 2 for symmetric linear molecules.
ROTATIONAL PARTITION FUNCTIONS:

TYPICAL PARTITION FUNCTION VALUES:
Molecule
H2
H35Cl
D35Cl
16O
2
CsI
H-C≡C-F
B(MHz)
1,824,300
312,991
161,656
43,101
708.3
9706
σ
2
1
1
2
1
1
qRot (300K)
1.71
20.0
38.7
72.5
8830
644
PARTITION FUNCTION COMMENTS:

ROTATIONAL LEVEL POPULATIONS – CO:
J
2J+1
Pi
0
1
1
1
0.00927
1
3
0.9816
2.945
0.02729
2
5
0.9459
4.730
0.04383
5
11
0.7573
8.330
0.07720
8
17
0.5131
8.723
0.08085
10
21
0.3608
7.578
0.07023
15
31
0.1082
3.353
0.03108
20
41
0.00204
0.8366
0.00775
25
51
0.00242
0.1235
0.00114
COMMENTS ON PREVIOUS SLIDE:

COMMENTS – CONTINUED:
Less than 1% of CO molecules are in the J=0
level at 300K.(More than 99.99% of CO
molecules are in the v=0 level at 300K)
P0 = 1/qRot The P0 value is small for many
linear molecules at room temperature. P0
values can be increased by lowering the
temperature of the molecules.
HCl AND DCl INFRARED SPECTRA:
The HCl and DCl spectra obtained in the lab
show features consistent with the results
presented here. These spectra are shown on
the next slides for consideration/class
discussion.
THE HYDROGEN ATOM:

THE HYDROGEN ATOM:
For the 3-dimensional PIAB we have:
3 Cartesian coordinates
3 quantum numbers required to describe E.
With problems involving rotation (especially
in 3 dimensions) and energies of electrons in
atoms, spherical polar coordinates (r,θ,φ)are
a more natural choice than Cartesian
coordinates. Why?
ATOMS AND ELECTRONIC ENERGIES:

COULOMBIC INTERACTIONS:
Class discussion of coulombic forces,
energies and “work terms” (simple
integration). Need for spherical polar
coordinates in treating the H atom.