Lecture 2 - Rotational spectroscopy Flashcards
What is rotational spectroscopy?
-Involves the rotation of molecules measured relative to a fixed axis in a lab.
-Very low energy transitions.
-Only done with gases at low pressure (important).
-Need low temps and press as too high will have too much collisions and the detail will decrease as lines become broad.
What is moment of intertia?
-Depends on the mass and how far away it is from the rotation axis.
-Large moments of inertia are called disks, most mass is away from the centre - example benzene ring.
-Small moments of inertia are rods, most mass sits on the rotation axis - example is a linear molecule.
-Inertia is given be I = mr^2
-Inertia also depends on the bond lengths and angles.
-An object can have 3 moments of inertia, rotation around 3 axes.
Around X, IA, has the smallest. Around Y, IB, has middle. Around Z, IC, has the largest. (These are all known as the DOF)
-Linear molecule has very small rotations around X axis, and so IA for linear molecules is 0, so only depends on IB and IC.
- So, linear molecules only have 2 DOF and is given by 3N-5
- Non-linear given by 3N-6.
What is angular momentum?
-The equivalent to linear momentum, instead of mass x velocity, angular momentum is moment of inertia x angular velocity (P=I x AV)
-Linear motion (a ball for example) is based on m x v. This is because how hard a ball is thrown depends on its weight and its velocity.
-Angular momentum is the same but something going round in circles, inertia is the mass and angular velocity is how fast its going.
-Angular momentum is quantized and so has a formula.
What is the rotational kinetic energy?
- The rotational kinetic energy is the kinetic energy of a rotation which contributes to the total kinetic energy of a system
- Normal kinetic energy is given by 1/2mv^2, rot KE is given by Erot = 1/2I x I x AV^2
-Rearrange P = I x AV for AV = P/I and sub this into the kinetic energy. - This gives E = BJ(J+1)
What is B in E = BJ(J+1)
B is the rotational constant
This can be divided to give in cm-1, so B = h/8(pi^2)cI
How is BJ(J+1) used?
-For example, if a molecule is being excited from J=0 to J=1 then J=1.
- E = BJ(J+1) = B(1+1) = 2B
-So the energy of J=1 is 2B
- For 2 its 6B
- For 3 its 12B.
-The lines on a spectrum will be taller as these numbers increase.
-Transition energy (energy needed to go from 1 state to another would be given by taking the 2 E’s away from each other)
How is the energy difference between neighbouring levels found?
DeltaE = DeltaE(j+1)-Ej
= B(J+1)(J+2) - BJ(J+1)
=2B(J+1)
As J increases, then spacing between energy levels increase.
The difference between J=0 and J=1 is 2B.
The difference between J=1 and J=2 is 4B and so on.
The difference keeps increasing by 2B.
What are the selection rules for rotational spectroscopy?
-Molecules must have a permanent dipole and it must change during rotation.
-So linear molecules must be of the opposite molecules (H-Cl)
- DeltaJ = (+/-) 1 but many states are occupied so many transitions possible.
-Also needs to be gases at low temps and pressures.
-Spectrum needs to be evenly spaced lines of 2B. (Intensity can increase as energy level increases)
-Bonds lengths can be calculated from I = mr^2
How do the peak intensities work?
-The intensity of each line (as J increases) will increase (BUT ALSO SPACED BY 2B) until a certain point, nut will then start dropping.
- This is due to the fact that higher energy levels wont have sufficient thermal energy (T) to be filled at room temp and low press (Boltzmann distribution)
How can the Boltzmann distribution be used?
The Boltzmann distribution can give the relative population of states.
N1/N0 = g1/g0 exp(DeltaE/kT)
Shows how much a state is populated over another.
Given as n0 = xn1
As the ground state will be more populated.
