Topic 3 Flashcards
What is the formula of moment of inertia I of a system about an axis passing through the centr mass?
Where mi is the mass of the ith particle and ri is the perpendicular distance from the axis.
![](https://s3.amazonaws.com/brainscape-prod/system/cm/362/267/012/a_image_thumb.png?1636118999)
Using moment of inertia equation for diatomic molecule when m1r1=m2r2?
When the rotational axis passes through the centre mass.
If m1r1=m2r2 and r1+r2=R what is the value or r1?
![](https://s3.amazonaws.com/brainscape-prod/system/cm/362/287/695/a_image_thumb.png?1636119653)
What is the equation of moment of inertia for diatomic molecule?
I=μR2
What is the expresion for rotational energy?
F(J)=BJ (J+1)
Where J is the rotational quantum number= 0, 1, 2, …
B is the rotational constant
How to calculate rotational constant in joule?
![](https://s3.amazonaws.com/brainscape-prod/system/cm/362/288/625/a_image_thumb.png?1636120430)
How to calculate rotational constant in hertz?
Since E=hv
![](https://s3.amazonaws.com/brainscape-prod/system/cm/362/288/741/a_image_thumb.png?1636120485)
How to calculate rotational constant in cm-1 ?
Since E=hc/λ, uce c in cm s-1
![](https://s3.amazonaws.com/brainscape-prod/system/cm/362/289/114/a_image_thumb.png?1636120558)
What are rotational selectrion rules?
- 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)
What are degenerate rotations?
Rotations around the y and z axes are indistinguishable and called degenerate rotations.
How do we use microwave spectra to calculate bond length?
B is inversely proportional to moment of inertia and μR2 so by knowing B from spectra and relative atomic masses we can calculate R
What it means by saying that Re is isotope independent?
That Re is determined by electron structure
What it means by saying B is isotope dependent?
That B depends on the reduced mass. And so spectra will have different spacings
Why in the absence of external magnetic fields each J level exhibit (2J+1)-fold degeneracy?
It is because for each of the rotational levels, there is acually a projection quantum number MJ and there are (2J+1) values of those. So those would actually have different energies if there were an external field.
Where is the most populated rotational level?
It occurs for dnJ / dJ=0
![](https://s3.amazonaws.com/brainscape-prod/system/cm/362/291/026/a_image_thumb.png?1636122192)