Rotational Spectroscopy

Question 1

Which region of EM spectrum do transitions correspond to?

Answer 1

The microwave and IR regions

Question 2

Why are measurements made in the gas phase?

Answer 2

Solid- molecules not free to rotate

Liquids- collisions occur to frequency for molecules to rotate freely enough

Question 3

What is rotational spectroscopy used for?

Answer 3

It can be used for identification and to measure molecular properties such as bond length.

Question 4

Moment of inertia is the resistance to rotation. What is the equation for moment of inertia?

Answer 4

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

Question 5

Rotational energy is the kinetic energy due to motion, what is the equation?

Answer 5

E= 1/2 I x angular velocity^2

Units: radians s-1

Question 6

What does quantum mechanics tell us about rotational levels?

Answer 6

They are quantised- molecules can only rotate with a discrete amount of energy

They are closely spaced - microwave region

Question 7

How are molecules treated so rotational spectra can be understood?

Answer 7

Treated as rigid rotors
Bond has fixed length
Rotation occurs around a centre of mass

Question 8

What is the energy of the rotational energy levels?

Answer 8

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)

Question 9

What does quantum theory tell us about the rotational energy levels?

Answer 9

J defines the permitted energy levels EJ

B determines the actual energy levels for a specific molecule

Question 10

What is the value of the rotational constant B?

Answer 10

B= h/ 8pi^2 x I x c

Units are s-1

Energy can be defined in terms of B, e.g. 20B

Question 11

What is the EJ for the lowest level?

Answer 11

For J=0

EJ= BJ(J+1)
=0
Therefore there is no rotational energy as the molecule is not rotating

Question 12

What happens to the gaps as rotational energy increases

Answer 12

The gaps between the energy levels increase with increasing rotational energy

Question 13

What does B the rotational constant depend on?

Answer 13

B is constant for a specific molecule and depends on the moment of interia, which depends on masses and bond length

Question 14

What is the equation for reduced mass?

Answer 14

RM= m1 x m2/ m1 + m2

Units are kg

Question 15

What is the dependence on of a small molecule, light on reduced mass, bond length, I, B, energy, energy gap

Answer 15

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

Question 16

What is the dependence on of a large heavy molecule on reduced mass, bond length, I, B, energy, energy gap

Answer 16

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

Question 17

What are the gross selection rules?

Answer 17

For absorption and emission there must be a change in dipole on rotation
- must have a permanent dipole

Question 18

What is the specific selection rule?

Answer 18

^J = +/- 1

This means that a transition is allowed only to the next rotational level

Question 19

Consider one molecule in rotational transitions.

Answer 19

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

Question 20

Rotational energy levels are closely spaced, what does this mean?

Answer 20

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

Question 21

What is the equal for population?

Answer 21

Population is proportional to (2J+1) e^ (-EJ/KT)

Number of states in each J level
Boltzmann distribution

Question 22

How do you calculate B from experimental data?

Answer 22

Calculate the energy of the energy gap and find this in terms of B (e.g. 2B) then find B.

Question 23

What is a non rigid diatomic molecule?

Answer 23

These have bond lengths that are not fixed
When a molecule rotates, it stretches
The more it rotates the more it stretches

Question 24

What does quantum mechanics tell us about the non rigid molecule EJ ?

Answer 24

EJ= B J (J+1) - D J^2(J+1)^2

^EJ-> J+1 = 2B (J+1) - 4D(J+1)^3

D= centrifugal distortion

Question 25

What can rotation properties be described by?

Answer 25

3 moments of inertia about 3 perpendicular axis

Question 26

How many rotational degrees of freedom do linear and non linear molecules have?

Answer 26

Non linear have 3 rotational degrees of freedom

Linear have 2 rotational degrees of freedom

Question 27

What moments of inertia do diatomic, linear rotors, spherical rotors, symmetrical rotors and asymmetric rotors have?

Answer 27

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

Question 28

What are the applications of RS?

Answer 28

To determine molecular structure by determining bond lengths and bond angles of gas phase samples

Question 29

What are the applications in interstellar chemistry?

Answer 29

You can identify interstellar molecules by specific rotational lines of emission or absorption

Question 30

When will energy be absorbed?

Answer 30

Energy is only absorbed when it matches exactly the energy different between the two adjacent transition energy levels

Question 31

What is centrifugal distortion?

Answer 31

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