Question 3 - Microwave and Rigid Rotor

Question 1

In a microwave spectrum, what is on the x and y axis?

Answer 1

y = transmittance
x = frequency

Question 2

Describe what is meant by the rigid rotor model.

Answer 2

The atoms are two point masses located at fixed distances from their centre of masses. The bond is like a rigid rod between them.

Question 3

Explain the form of the IR spectrum in terms of the results based on a rigid rotor.

Answer 3

According to the QM analysis of the rigid rotor model the rotational energy levels have energies E = h B J (J+1)
This gives rise to energy levels at 0, 2hB, 4hB, 6hB etc
Therefore the energies of transitions are 0, 2hB, 4hB, 6hB etc
This gives rise to a spectrum of sharp peaks of regular spacing 2hB Hz

Question 4

From the spacing between the peaks in an IR spectra how is the rotational constant calulated?

Answer 4

B = spacing / 2

B = rotational constant, S-1

Question 5

How is bond length calculated?

Answer 5

B = h / 8(π)^2 I

B = rotational contant
h = planck’s constnat
I = inertia

r = (I / μ)^-1/2

r = bond length

Question 6

Assuming the bond length is the same for H2Cl35 predict the spacing of the peaks on its spectrum.

Answer 6

Reduced mass calculation (H = m1 = 2, Cl = m2 = 35)

Moment of inertia, I = μ x r^2

B = h / 8π^2 I

spacing between peaks = 2B Hz