Rotational Spectroscopy Flashcards
Which region of EM spectrum do transitions correspond to?
The microwave and IR regions
Why are measurements made in the gas phase?
Solid- molecules not free to rotate
Liquids- collisions occur to frequency for molecules to rotate freely enough
What is rotational spectroscopy used for?
It can be used for identification and to measure molecular properties such as bond length.
Moment of inertia is the resistance to rotation. What is the equation for moment of inertia?
Centre of gravity c: m1r1=m2r2
I = m1r1^2 + m2r2^2
Units= kgm^2
This can be rewritten as I= RM r^2
RM= m1 x m2/ m1 + m2 ( reduced mass) -kg
r is bond length in m
Rotational energy is the kinetic energy due to motion, what is the equation?
E= 1/2 I x angular velocity^2
Units: radians s-1
What does quantum mechanics tell us about rotational levels?
They are quantised- molecules can only rotate with a discrete amount of energy
They are closely spaced - microwave region
How are molecules treated so rotational spectra can be understood?
Treated as rigid rotors
Bond has fixed length
Rotation occurs around a centre of mass
What is the energy of the rotational energy levels?
EJ = BJ(J+1)
Where J= 0,1,2,3…
EJ= energy of rotational levels (cm-1)
B= rotational constant (cm-1)
J= rotational quantum number (energy level number)
^EJ -> J+1= 2B(J+1)
What does quantum theory tell us about the rotational energy levels?
J defines the permitted energy levels EJ
B determines the actual energy levels for a specific molecule
What is the value of the rotational constant B?
B= h/ 8pi^2 x I x c
Units are s-1
Energy can be defined in terms of B, e.g. 20B
What is the EJ for the lowest level?
For J=0
EJ= BJ(J+1)
=0
Therefore there is no rotational energy as the molecule is not rotating
What happens to the gaps as rotational energy increases
The gaps between the energy levels increase with increasing rotational energy
What does B the rotational constant depend on?
B is constant for a specific molecule and depends on the moment of interia, which depends on masses and bond length
What is the equation for reduced mass?
RM= m1 x m2/ m1 + m2
Units are kg
What is the dependence on of a small molecule, light on reduced mass, bond length, I, B, energy, energy gap
A small light molecule has a low reduced mass
- Less resistance to rotation so a small I
- Short bond length so a larger rotational energy
- Large B
- Large energy
- Large energy gap
What is the dependence on of a large heavy molecule on reduced mass, bond length, I, B, energy, energy gap
A large molecule heavy has a high reduced mass
- More resistant to rotation so large I
- Long bond length so a smaller rotational energy
- Small rotational constant
- Small energy
- Small energy gaps
What are the gross selection rules?
For absorption and emission there must be a change in dipole on rotation
- must have a permanent dipole
What is the specific selection rule?
^J = +/- 1
This means that a transition is allowed only to the next rotational level
Consider one molecule in rotational transitions.
It is one specific rotational level J of energy EJ
It can undergo an absorption transition only to the next level J+1
This is done by absorbing a photon only of energy equal to the gap ^EJ-> J+1
Rotational energy levels are closely spaced, what does this mean?
This means molecule can occupy a range of different J levels
A transition can occur from each populated level (absorbing a photon equal to the gap)
The spectrum will show several lines
Intensities depend on population of levels
What is the equal for population?
Population is proportional to (2J+1) e^ (-EJ/KT)
Number of states in each J level
Boltzmann distribution
How do you calculate B from experimental data?
Calculate the energy of the energy gap and find this in terms of B (e.g. 2B) then find B.
What is a non rigid diatomic molecule?
These have bond lengths that are not fixed
When a molecule rotates, it stretches
The more it rotates the more it stretches
What does quantum mechanics tell us about the non rigid molecule EJ ?
EJ= B J (J+1) - D J^2(J+1)^2
^EJ-> J+1 = 2B (J+1) - 4D(J+1)^3
D= centrifugal distortion
What can rotation properties be described by?
3 moments of inertia about 3 perpendicular axis
How many rotational degrees of freedom do linear and non linear molecules have?
Non linear have 3 rotational degrees of freedom
Linear have 2 rotational degrees of freedom
What moments of inertia do diatomic, linear rotors, spherical rotors, symmetrical rotors and asymmetric rotors have?
Diatomic, linear rotors has 2 equal and 1 zero
Spherical rotors have 3 equal
Symmetrical rotors have 2 equal and 1 different
Asymmetric rotors have 3 different
What are the applications of RS?
To determine molecular structure by determining bond lengths and bond angles of gas phase samples
What are the applications in interstellar chemistry?
You can identify interstellar molecules by specific rotational lines of emission or absorption
When will energy be absorbed?
Energy is only absorbed when it matches exactly the energy different between the two adjacent transition energy levels
What is centrifugal distortion?
As energy increases, the molecule rotates faster and the bond lengths get slightly longer
This causes the spacing between spectrum lines get smaller as J increases
