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Flashcards in Rotational (Microwave) Spectroscopy Deck (41)
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Rotation of molecules?

3 axes of rotation, movement of inertia (I) defines energy of rotation
Ia = Ib, Ic about the molecular axis is very small


Energy of rotation depends on?

Mass of atoms
Distance between atoms
Angular velocity


Selection rules for rotational spectroscopy?

In order to interact with EM radiation, the molecule must possess an electric dipole which can oscillate at the frequency of the radiation – also called a transition moment


Gross selection rule?

Molecules must possess a permanent dipole, only heteronuclear diatomics give a pure rotational spectrum


Specific selection rule?

Only transitions between adjacent energy levels can occur DeltaJ ± 1


Expression for rotational energies?

EJ = BJ(J+1)


Lower reduced mass?

A lower reduced mass will give a larger rotational constant, Thus,H2 ,whichhasthe lowest reduced mass of any molecule, will have a large rotational constant


High reduced mass or large r?

Molecules with a high reduced mass, or large r have small B constants, rotational levels are not resolved for very large molecules because they are so close together in energy


Absorption spectroscopy?

Spectroscopy looks at transitions, we know the energies and the selection rules, we can predict what the spectrum will look like, absorption occurs when the photon energy matches the difference between energy levels


Line spacing in rotational (microwave) spectroscopy?

The levels get further apart as J increases, the spectrum therefore consists of a series of equally spaced lines – separation is 2B, measuring B from the spectrum --> calculate the moment of inertia,
knowing m1 and m2 --> calculate the bond length


Why are not all the intensities of the lines the same?

We have to look at the occupancy of the levels, need to look at the population and degeneracy


What is degeneracy?

Degeneracy – number of levels with exactly the same energy


What does the intensity of the absorption peak depend on?

The intensity of the absorption peak depends on the number of molecules that absorb the radiation i.e. the number in the energy level – the population, usually fewer molecules
in higher energy states, more likely to have higher E states populated if deltaE is small


Trends in Boltzmann distribution?

As exponential term tends to 0 where n upper = n lower, change in energy is very small or T is very large
If exponential term is large, the negative sign means n upper << n lower, change in energy is very large or T is very small


Boltzmann and populations at higher temperature?

At higher temperatures, there is higher population of higher levels


Boltzmann and populations when change in energy is large?

If change in energy is large, only the lowest energy levels will have significant populations


Boltzmann and populations when change in energy is small?

If change in energy is small, many energy levels will be populated


Population trends?

The population falls off exponentially as change in energy increases


Implications of the Boltzmann Distribution when the energy gap is large?

Large energy gap - most population will be in the ground state unless the temperature is very high, e.g. at room temperature, most molecules are in their ground electronic state - energy spacing between electronic states is large compared to kBT


Implications of the Boltzmann Distribution when the energy gap is small?

Small energy gap - higher levels are populated at moderate temps e.g. at room temperature, there is a significant population of higher rotational levels - energy spacing between rotational states is comparable with (or smaller than) kBT


Implications of the Boltzmann Distribution when two levels have the same degeneracy?

For two levels with same degeneracy as T tends to infinity, then populations of upper and lower levels becomes the same, the upper level can never have a higher population than the lower state in a solely thermal distribution


How to account for degeneracy?

Also need to account for the degeneracy – number of states with the same energy,
modify Boltzmann with a simple term reflecting this: gupper/glower


Example of degenerate orbital?

2p orbitals, 2 electrons in each orbital – all have the same energy


Degeneracy of rotational levels?

Rotational energy levels are also degenerate, degeneracy, for a rigid rotor, there will be a number of levels with identical energy


Rotational levels?

Rotational levels: (2J + 1) fold degenerate, in this course, the degeneracy factor is only relevant for populations in Rotational spectroscopy


What does intensity of absorption peak depend on?

Intensity of the absorption peak depends on how many molecules are in the J’th state,


If change in energy is much less than Boltzmann constant?

If change in energy << kBT so the population ratio for these levels is determined largely by the ratio of the degeneracies


What happens to the degeneracy as J increases?

The degeneracy increases as J increases; However, the value of change in energy also increases and eventually becomes greater than kBT - the ratio of the populations becomes < 1 at high values of J, overall, this means that the population of molecules is spread throughout many rotational levels


Occupancy of levels?

Occupancy of levels rises and
passes through a maximum
– just as observed in the spectra


Diatomic effects of isotopes?

Isotopic substitution does not affect electronic binding, and therefore inter-nuclear distance, r unchanged,
change in mass --> change in I
It is the reduced mass that is affected by isotopic substitution