rotational spectroscopy

Question 1

what type of spectroscopy is rotational spectroscopy?

Answer 1

transmission

Question 2

how does transmission spectroscopy work?

Answer 2

light source passes through a molecule which absorbs certain wavelengths / colours, and transmits others

Question 3

what kind of EM radiation is used in rotational spectroscopy?

Answer 3

microwave, as ΔE is ~1-10 cm-1, quite small

Question 4

is a molecules moves in a direction x, y or z, what does this imply?

Answer 4

means the molecule has kinetic energy

Question 5

how is speed of rotation determined, and why is speed specifically used?

Answer 5

speed = distance / rotation time
where distance = circumference = 2πr

Question 6

angular velocity, ω definition

Answer 6

angular velocity is = for all points of a rigid rotating body, defined in terms of distance from the centre and translational velocity: v = rω

Question 7

adapt the kinetic energy equation for angular velocity

Answer 7

E = 1/2mv^2
= 1/2m(rω)^2
= 1/2mr^2*ω^2

now E = kinetic energy of a single particle rotating around a fixed axis

Question 8

how is angular momentum conserved?

Answer 8

it is conserved when no net force is acting to slow the rotation - once rotation starts energy is constant, but velocity can change so it can increase if resistance forces are minimised

Question 9

give the equation for moment of inertia, I

Answer 9

I = Σmr^2 or better I = μr^2
where m = mass, μ = reduced mass and r = distance

Question 10

moment of inertia, I definition

Answer 10

energy of rotation in a certain direction

Question 11

how many moments of inertia do molecules have?

Answer 11

3, one for each axis
- however these moments of inertia are only deemed significant if atoms change position during rotation

Question 12

what 3 factors does rotational energy depend on?

Answer 12

atomic mass, distance between atoms, angular velocity

Question 13

what is the purpose of reduced mass, μ?

Answer 13

in most molecules, mass is not evenly distributed, so reduced mass is used to simplify a 2 body system into a 1 body system

Question 14

outline the rigid motor model

Answer 14

using reduced mass, the molecule/diatomic/bond has been simplified to a single point mass, where the centre of the molecule = the centre of the bond, closer to the heavier atom
when the bond is rotated, the heavier atom hardly moves, the smaller atom spins around it - as its a rigid rotor, this assumes bond length doesn’t change with rotation

Question 15

forbidden transition definition

Answer 15

when transitions between energy levels have a 0% chance of occurring, based on quantum mechanical calculation

Question 16

what is the purpose of selection rules?

Answer 16

to inform us about which transitions are allowed and which aren’t

Question 17

what are the 2 types of selection rule?

Answer 17

gross and specific

Question 18

outline the purpose of the gross selection rules for rotational spectroscopy

Answer 18

they tell us if a molecules will have a rotational spectra, in terms of molecular properties for particular types of absorption

Question 19

outline the purpose of the specific selection rules for rotational spectroscopy

Answer 19

they tell us which transitions are allowed, in terms of levels between which transitions can take place

Question 20

what molecules can undergo rotational spectroscopy?

Answer 20

the molecule must possess an electric dipole that can oscillate at the frequency of the radiation, in order to interact with the EM radiation used
- this is an example of a gross selection rule

Question 21

can homonuclear diatomics undergo rotational spectroscopy?

Answer 21

no, they have no permanent dipole

Question 22

can heteronuclear diatomics undergo rotational spectroscopy?

Answer 22

yes, they do have permanent dipoles

Question 23

what transitions are allowed in rotational spectroscopy?

Answer 23

only transitions between adjacent energy levels (ΔJ = +/-1) - where J = energy levels
- this is an example of a specific selection rule

Question 24

what is B?

Answer 24

rotational constant, takes 3 forms:
- energy = h^2/(8π^2I), units J
- wavenumber = h/(8π^2Ic), units cm^-1
- frequency = h/(8π^2I), units Hz

necessary to calculate the energy of rotational levels

Question 25

what happens to energy levels as B changes?

Answer 25

they will also change, as their related to molecular mass and bond length - therefore all molecules have unique energy levels, like a signature/fingerprint

Question 26

what kind of photon will be absorbed?

Answer 26

the photon must match the difference between energy levels - this means energy of photons absorbed is related to bond length and molecular mass

Question 27

what is on the x and y axes of a spectra?

Answer 27

y-axis = intensity/absorption x-axis = energy

Question 28

when E = 0, what do we expect to see on a spectra and why?

Answer 28

when E=0, no energy is present, meaning there is no light, so no absorption or activity at all will be recorded

Question 29

what do we expect to see on a spectra as wavelength of light is changed?

Answer 29

as energy/wavelength of light changes, some will be absorbed if it matches with the energy needed for available transitions - this is what peaks show

Question 30

how does the difference between photon energies change on the spectra?

Answer 30

it doesn't, photon energy/peaks will increase in equal steps because ΔE increases in equal steps (ΔE - ΔE = 2B)

Question 31

how does isotopic substitution affect the spectra produced?

Answer 31

it doesn't affect electronic binding, but it does affect mass - change in mass means change in moment of inertia, which means change in B which changes ΔE - on a spectra this could appear as a series of many slightly overlapping, differently spaced lines per isotope present, intensity depending on abundance

Question 32

how does isotopic substitution affect diatomics?

Answer 32

for heterodiatomics, one atom is larger than the other - there is a much larger impact if the lighter element is substituted with an isotope, as this has a larger impact on the mass ratio - e.g. if hydrogen were swapped with dueterium, μ woudl change a lot

Question 33

give the limitations of rigid rotor model

Answer 33

we assume through the rigid rotor model that bond lengths are fixed, whereas in real life this isn't the case faster rotation causes bonds to stretch, which increases J values so 2B is not longer the distance between 2 peaks, the gap decreases as bonds are stretched

Question 34

how do we account for the stretching of bonds during rotation?

Answer 34

centrifugal distortion constant D

Question 35

what are the 4 types of polyatomic molecules?

Answer 35

linear molecules symmetric tops spherical tops asymmetric rotors

Question 36

give an example of linear polyatomics and describe their moments of inertia

Answer 36

e,g, CO2. C2H2 these have 2 moments of inertia where one = 0: Ib = Ic, Ia ~ 0 - treated just like 2 body molecules

Question 37

give an example of symmetric top polyatomics and describe their moments of inertia

Answer 37

e.g. NH3, CH3F overall 3 moments of inertia Ib = Ic =/= Ia, but Ia =/= 0

Question 38

give an example of spherical top polyatomics and describe their moments of inertia

Answer 38

e.g. CH4 3 moments of inertia Ia = Ib = Ic - however these have no dipoles, so usually have no rotational spectra anyway

Question 39

give an example of asymmetric rotors and describe their moments of inertia

Answer 39

e.g. H2O, NO2 have 3 moments of inertia, most complex Ia =/= Ib =/= Ic, also have different B depending on axis of rotation - introducing more axis of rotation requires more quantum numbers, very complicated)

Question 40

why do peaks have different intensities?

Answer 40

this depends on population and degeneracy: - absorption is related to the number of molecules in that rotational state which can be promoted to the next state via photon absorption, so greater population of a state of excitation means greater number of molecules that can absorb radiation, means greater intensity - degeneracy of higher energy orbitals means there are more pathways into these orbitals so its possible for more molecules to absorb photos and excite themselves into that state, so greater intensity

Question 41

how can degeneracy be calculated for rotational levels?

Answer 41

formula 2J +1

Question 42

how does degeneracy affect population of rotational energy levels?

Answer 42

as J increases, degeneracy increases, and so does ΔE, so eventually ΔE>>KbT so population ratio becomes ~ 1 at high J values

Question 43

explain the boltzmann-like shape of rotational spectra

Answer 43

at lower J, when ΔE is small, the exponential tends to 1, so degeneracy has a greater impact and dominates, so we see linear increase on graph whereas at higher J, ΔE is larger and so the exponential term dominated, tending towards 0, so we see exponential decrease