Quiz 4 Slides

Question 1

Each mass will experience a restoring force that is proportional to its displacement from equilibrium

Answer 1

Hooke’s Law

Question 2

Does harmonic oscillator obey hooke’s law?

Answer 2

yes

Question 3

force constant of the bond is equivalent to the ___ of the potential energy function

Answer 3

curvature

Question 4

masses m1 and m2 each have

Answer 4

displacements x1 x2 assuming simple harmonic motion oscillating as a cosine function of time

Question 5

since both standard differential equations have to be true simultaneously, they also show

Answer 5

that each mass oscillates with the same frequency and phase constant; each mass goes through its equilibrium position simultaneously

Question 6

transition spacings are all what frequency of oscillation

Answer 6

v0

Question 7

resulting spectrum from harmonic oscillator has how many bands

Answer 7

1 abs band

Question 8

fundamental vibrational frequency

Answer 8

transition v = 0 to v=1

Question 9

harmonic oscillator approach is good for

Answer 9

very small displacements about equilibrium; first approximation to real spectra; not much else

Question 10

a better approximation to physical reality from harmonic oscillator needs what

Answer 10

a more realistic potential function

Question 11

morse potential

Answer 11

empirical function where Vx approaches infinity as x approaches 0, is asymptotically approaching a constant value De

Question 12

correction factor that lowers each energy level relative to the harmonic energy levels

Answer 12

anharmonicity constant

Question 13

result of anharmicity constant

Answer 13

energy levels of oscillatornot evenly spaced

Question 14

transitions that appear with decreasing intensity at fundamental vibrational frequencies 2, 3, etc

Answer 14

overtones

Question 15

transition that occurs more rapidly if temp is raised

Answer 15

hot bands

Question 16

what causes hot bands

Answer 16

higher v states are more populated at higher temp

Question 17

anharmonic oscillator equation overestimates De by 20% because…

Answer 17

it assumes a linear estimates – change in energy constant with v, which is not true, especially at higher v

Question 18

energy levels equally spaced on the ladder

Answer 18

harmonic oscillator

Question 19

energy levels get closer as energy increases; near dissociation, energy becomes continuous

Answer 19

real molecule

Question 20

degrees of freedom also refers to

Answer 20

number of possible fundamental vibrations in a molecule

Question 21

three of the possible fundamental vibrations are simply…

Answer 21

simultaneous, in phase translations of each atom together along one of the directional coordinates

Question 22

do translations correspond to real molecular vibrations?

Answer 22

nope

Question 23

three more possible fundamental vibrations exist that simply refer to…

Answer 23

rotation of each atom about 3 principle axes of rotation

Question 24

does rotation correspond to real molecular vibration

Answer 24

no

Question 25

to find translational movements for non-linear molecules

Answer 25

subtract 3 degrees freedom

Question 26

for rotational movements of nonlinear molecules

Answer 26

subtract 3 degrees of freedom around its principle axes

Question 27

for linear molecule’s translational movements

Answer 27

subtract three degrees of freedom

Question 28

for a linear molecules rotational movement

Answer 28

subtract 2 degrees of freedom

Question 29

do linear molecules have rotation around long axis?

Answer 29

no real discernable rotation along major axis

Question 30

linear polyatomic fundamental molecular vibration

Answer 30

3N-5

Question 31

nonlinear polyatomic fundamental molecular vibrations

Answer 31

3N-6

Question 32

of the possible fundamental molecular vibrations, how many are caused by bond stretching?

Answer 32

N-1

Question 33

of the possible fundamental molecular vibrations, how many will be caused by bond bending

Answer 33

2N-5 nonlinear, 2N-4 linear

Question 34

molecular motion in which all atoms move in phase and with the same frequency

Answer 34

normal modes of vibration

Question 35

types of normal mode molecular vibrations: stretching

Answer 35

symmetric and asymmetric

Question 36

types of normal mode molecular vibrations: bending

Answer 36

in plane rocking, in plane scissoring, out of plane wagging, out of plane twisting

Question 37

strength of polarity in chemical bond described by

Answer 37

the dipole moment

Question 38

chemical bonds and vibrations can be described on the basis of

Answer 38

molecular symmetry relative to a symmetry element in the molecule

Question 39

in order to absorb IR radiation, molecular vibration must

Answer 39

cause a change in the permanent dipole moment either parallel or perpendicular to a symmetry element in molecule

Question 40

is symmetric stretching vibration ir active

Answer 40

no

Question 41

IR activity requires

Answer 41

change in permanent dipole moment of the chemical bond

Question 42

very strong in IR spectrum

Answer 42

polar bonds with large dipole moments

Question 43

non polar bonds in IR spectrum

Answer 43

weak or absent

Question 44

when harmonic oscillator condition is relaxed

Answer 44

overtone vibrations become permissible

Question 45

also appear due to anharmonicity

Answer 45

combination and difference bands

Question 46

in addition to overtone vibrations, these bands also appear due to anharmonicity

Answer 46

combination and difference

Question 47

appear at the value due to the sum of 2+ fundamental molecular vibrations

Answer 47

combination bands

Question 48

arise from ground vibrational levels

Answer 48

combination bands

Question 49

binary combination level involves

Answer 49

2 different normal coordinates with nonzero quantum numbers

Question 50

1 photon excites 2 different vibrations simultaneously if

Answer 50

that photon has an energy approx. equal to the sum of energies needed to excite them separately

Question 51

do not arise from fundamental molecular vibrations

Answer 51

difference bands

Question 52

difference bands vs combination band strength

Answer 52

difference are weaker

Question 53

difference bands at low temps

Answer 53

disappear

Question 54

difference transition occurs from

Answer 54

excited level of one transition to that of another

Question 55

intensity of difference transition varies with

Answer 55

the population of the excited state

Question 56

when the energy of an overtone or combo band happens to have the same value as the energy of a fundamental vibration

Answer 56

accidental degeneracy

Question 57

Fermi resonance

Answer 57

accidental degeneracy results in sometimes 2 relatively strong bands where only one fundamental was expected; two observed occur at higher and lower energies than the expected

Question 58

two energy levels in fermi resonance interact

Answer 58

on quantum mechanical level due to anharmonic terms in potential energy

Question 59

does fermi resonance energy difference have to be big

Answer 59

no

Question 60

vibrations in fermi resonance should be

Answer 60

able to couple via anharmonic terms, with overtone and fundamental of same symmetry

Question 61

vibrations which involve large amplitudes of isotopically labelled atom should

Answer 61

shift by the greatest amount

Question 62

isotopic mass difference vs wavenumber shift

Answer 62

larger IMD greater WNS

Question 63

For H-D substitution new vibrational wavenumber of D substituted bond will always

Answer 63

be shifted to lower energy relative to H sub species by factor of 1/sqrt2

Question 64

certain sub molecular groups of atoms consistently produce vibrational bands in characteristic frequency regions of vibrational spectrum

Answer 64

group frequencies

Question 65

what causes group frequencies

Answer 65

coupling of oscillating dipole moments

Question 66

group frequencies can be very sensitive to

Answer 66

both config and conformation of local molecular groupings

Question 67

very sensitive probe for molecular structure

Answer 67

IR spectroscopy