Rotational Spectroscopy

Question 1

What happens in a rotational transition?

Answer 1

Leads to changes in the rotational state of the molecule

Question 2

Where does rotational spectroscopy occur?

Answer 2

In the microwave + far infrared region of the spectrum

Question 3

What state is rotational spectroscopy measured in?

Answer 3

Usually in the gas phase so the molecules are free to rotate

Question 4

What is meant by a ‘rigid rotor’?

Answer 4

Molecules are treated as rigid rotors i.e. the bond length doesn’t change during the rotation

Question 5

State the reduced mass of a single molecule.

Answer 5

1.66 x 10^-27 kg

Question 6

State the equation for the moment of inertia (I).

Answer 6

I = uro^2

u = (m1m2) / m1 + m2 
ro^2 = bond length in pico or nanometers

Question 7

State the units for the moment of inertia equation.

Answer 7

I: kgm^2

ro^2: m^2

Question 8

State the typical value for a solution to the moment of inertia equation.

Answer 8

In the range 10^-45 –> 10^-46 kgm^2

Question 9

What do we need to know for linear motion?

Answer 9

Only need to know the mass for inertia

Question 10

What do we need to know for rotational motion?

Answer 10

We need to know BOTH mass + distance

Question 11

What are the allowed rotational energy levels?

Answer 11

Given by Ej = hBJ (J+1)

Ej = energy of the jth rotational energy level
B = rotational constant in Hz
J = rotational quantum number
h = Planck's constant

Question 12

State the rotational constant (B) equation.

Answer 12

B = h / 8pi^2 I

Question 13

J quantum number

Answer 13

Rotational quantum number that takes +ve integer values

Question 14

State the TWO rotational selection rules.

Answer 14

1. Molecule must possess a permanent dipole moment

2. ∆J = +- 1 i.e. the quantised energy level must either increase or decrease by 1

Question 15

Does the molecule actually behave as a rigid rotor? Explain.

Answer 15

Bond length will actually increase as the molecule rotates, assuming bond length is fixed is inaccurate.

Question 16

How do we account for non-rigid rotors?

Answer 16

Ej = hBJ (J+1) - DJ^2 (J+1)^2

Where D is the centrifugal distortion coefficient.

Question 17

State the noticeable features of a rotational spectrum (3).

Answer 17

1. Base line is at the top
2. Intensity of absorptions rises, passes through a maximum + then falls
3. Series of regularly spaced absorptions as absorption energies increase by integer values