Topic 3

Question 1

What is the formula of moment of inertia I of a system about an axis passing through the centr mass?

Answer 1

Where m_i is the mass of the i^th particle and r_i is the perpendicular distance from the axis.

Question 2

Using moment of inertia equation for diatomic molecule when m₁r₁=m₂r₂?

Answer 2

When the rotational axis passes through the centre mass.

Question 3

If m₁r₁=m₂r₂ and r₁+r₂=R what is the value or r₁?

Answer 3

Question 4

What is the equation of moment of inertia for diatomic molecule?

Answer 4

I=μR²

Question 5

What is the expresion for rotational energy?

Answer 5

F(J)=BJ (J+1)

Where J is the rotational quantum number= 0, 1, 2, …

B is the rotational constant

Question 6

How to calculate rotational constant in joule?

Answer 6

Question 7

How to calculate rotational constant in hertz?

Answer 7

Since E=hv

Question 8

How to calculate rotational constant in cm^-1 ?

Answer 8

Since E=hc/λ, uce c in cm s^-1

Question 9

What are rotational selectrion rules?

Answer 9

• A molecule must have a permanent dipole moment in order to exhibit a pure rotational spectrum.
• Transitions occur for ΔJ=±1
• Transitions observed at F (J+1) - F(J)= 2B (J+1)

Question 10

What are degenerate rotations?

Answer 10

Rotations around the y and z axes are indistinguishable and called degenerate rotations.

Question 11

How do we use microwave spectra to calculate bond length?

Answer 11

B is inversely proportional to moment of inertia and μR² so by knowing B from spectra and relative atomic masses we can calculate R

Question 12

What it means by saying that R_e is isotope independent?

Answer 12

That R_e is determined by electron structure

Question 13

What it means by saying B is isotope dependent?

Answer 13

That B depends on the reduced mass. And so spectra will have different spacings

Question 14

Why in the absence of external magnetic fields each J level exhibit (2J+1)-fold degeneracy?

Answer 14

It is because for each of the rotational levels, there is acually a projection quantum number M_J and there are (2J+1) values of those. So those would actually have different energies if there were an external field.

Question 15

Where is the most populated rotational level?

Answer 15

It occurs for dn_J / dJ=0

Question 16

To what intensity of a rotational transition is proportional?

Answer 16

Question 17

Why thr J_max value is furter in the spectrum than expected?

Answer 17

Because the absorption spectral profile is governed by population of lower levels and the J dependence of the transition strength

Question 18

Are molecules rigid?

Answer 18

Molecules are not rigid rotors, their bonds stretch slightly during rotation

Question 19

How does centrifugal distortion affects energy expression?

Answer 19

Where D is the centrifugal distortion constant in cm^-1, F(J) value is lower

Question 20

How to calculate vibrational frequency, ω_e ?

Answer 20

Question 21

If we have values of ΔF(J) how can we finf values of B and D?

Answer 21

We plot ΔF(J)/(J+1) against (J+1)², this will give the intercept as 2B, and the slope as -4D