Table of Contents
What is Sigma in rotational partition function?
Rotational partition function: text derives rotational partition function as: sigma is the symmetry number. σ = 1 for heteronuclear diatomic (e.g. H-Cl, C-O) σ = 2 for homonuclear diatomic (e.g. N-N, O-O)
What is the order of magnitude of rotational partition function?
In general, the various are of order 10 3 K ; for instance, in the case of C O 2 , which was cited in footnote 15, Θ 1 = Θ 2 = 960 K , Θ 3 = 1 , 990 K , and Θ 4 = 3 , 510 K.
What is rotational degeneracy?
The degeneracy describes the fact that some levels have exactly the same energy and this depends the value of the angular momentum rotational quantum number J. The number of degenerate levels is given by the multiplicity 2J+1.
What is a partition function?
In physics, a partition function describes the statistical properties of a system in thermodynamic equilibrium. Partition functions are functions of the thermodynamic state variables, such as the temperature and volume.
What are P and R branches?
The rotational selection rule gives rise to an R-branch (when ∆J = +1) and a P-branch (when ∆J = -1). Each line of the branch is labeled R(J) or P(J), where J represents the value of the lower state.
How do you calculate J Max?
The population of the J = 1 level decreases as the energy level separation (i.e. 2B) increases. For example, at 300K, B = 5 cm-1 → kBT = 208.5 cm-1 → Jmax = 4 (which corresponds to the 4→5 transition).
What is the degeneracy of rotational levels?
The degeneracy describes the fact that some levels have exactly the same energy and this depends the value of the angular momentum rotational quantum number J . The number of degenerate levels is given by the multiplicity 2 J + 1 .
What is rotational energy level?
Rotational Energy Levels: For a nonlinear molecule the rotational energy levels are a function of three principal moments of inertia IA, IB and IC. These are moments of inertia around three mutually orthogonal axes that have their origin (or intersection) at the center of mass of the molecule.
What are PQ and R branches of vibration rotation spectrum?
On the high frequency side of the Q-branch the energy of rotational transitions is added to the energy of the vibrational transition. This is known as the R-branch of the spectrum for ΔJ = +1. The P-branch for ΔJ = −1 lies on the low wavenumber side of the Q branch.
How do you calculate rotational temperature?
is the rotational constant, I is a molecular moment of inertia, h is the Planck constant, c is the speed of light, ħ = h/2π is the reduced Planck constant and kB is the Boltzmann constant….Rotational temperature.
| Molecule | (K) |
|---|---|
| F2 | 1.27 |
| HF | 30.2 |
| HCl | 15.2 |
| CO2 | 0.561 |
How to separate the rotational partition function from other degrees of freedom?
Separation of the rotational partition function from the partition functions of other degrees of freedom does not only require consideration of nuclear spin states, but also the assumption that the moment of inertia is the same for all rotational states. This is generally true if the molecule behaves as a rigid rotor.
What is the nuclear-rotational partition function?
As a result, the nuclear-rotational partition function is given by the product of the respective partition functions, divided by a symmetry number γ that denotes the number of physically indistinguishable configurations realized during one complete rotation of the molecule: 13 compare with equation ( 27 ).
What is the license for the rotational partition function?
6.4: Rotational Partition Function is shared under a CC BY-NC 3.0 license and was authored, remixed, and/or curated by Gunnar Jeschke via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. Was this article helpful? There are no recommended articles.
What is the partition function in chemistry?
The partition function is a sum over states (of course with the Boltzmann factor β multiplying the energy in the exponent) and is a number. Larger the value of q, larger the number of states which are available for the molecular system to occupy.