Rotational Energy of Diatomics Flashcards
Rigid rotator energy
E = J(J+1)ℏ/2I
Inertia for diatomic
I=μr^2
Energy for rigid rotator also commonly written as
E=hcBJ(J+1)
Where B is rotational constant
Rotational constant, B equation
B=ℏ/(4picI)
Where I is the moment of inertia
Selection rule:
Since energy of photon produced is equal to energy of the energy gap then angular momentum is conserved, as such Delta J =1
Change in energy level
Simplified to 2BJ
How can rotations be observed on an IR graph
When molecule rotates it has an apparent change in dipole which is limited to one energy level
Spacing between peaks on an IR spectrum equal to
2B
Number of degenerate energy levels given by
2J+1, however high energy levels obviously required which is unlikely according to Boltzmann distribution
How many branches are on an IR spectrum and what are they?
There are 3: P, Q and R
Q branch on a spectrum
Q branch will be in the centre where absorbance = 0
R branch on a spectrum
Where wavenumber is reduced since rotational level has been reduced by 1
P branch on a spectrum
Where wavenumber is increased since rotational level has been increased by 1
Do liquids and solids have a V-R spectrum
No only gases as they are the only ones which have molecules that can rotate so liquids and solids have only the Q branch
How to solve for bond length?
Calculate separation between energy levels, this is equal to 2B, then use equations for moment of inertia and B to solve for bond length.
