The molecular population is :
Proportional to \((2J + 1)e^{-E/kT}\)
The population of a rotational level J at thermal equilibrium follows the Boltzmann distribution weighted by the degeneracy of the level: \(N_{J} \propto g_{J}e^{-E_{J}/kT}\).
A rotational level J has \(2J + 1\) degenerate states (\(M_{J} = -J, \dots, +J\)), so \(g_{J} = 2J + 1\) and \(N_{J} \propto (2J + 1)e^{-E_{J}/kT}\), with \(E_{J} = hcBJ(J+1)\).
The degeneracy factor makes the population rise at low J, while the exponential factor makes it fall at high J, which gives the familiar maximum in rotational band intensities.
An inverse degeneracy factor has no physical basis, and dividing by \(e^{-E/kT}\) (or multiplying by \(e^{E/kT}\)) would make higher-energy levels more populated without limit, contrary to the Boltzmann law.
Therefore the population is the product of the degeneracy and the Boltzmann factor.
Hence, Proportional to \((2J + 1)e^{-E/kT}\).
Important Questions from Mixed Topic (MH-SET)
.................... is a client server application that identifies each host on the internet with a unique user-friendly name.
Every OS has a ................ or .......... which primarily resides in the main memory of the computer to perform some of the basic functions of the OS.
(i) Kernel
(ii) Interface
(iii) Nucleus
(iv) Compiler
Codes:
Which of the following are referred to as low level language?
(i) Machine language
(ii) Assembly language
(iii) High level language
(iv) Natural language
Codes:
Match the following:
List I List II (a) New York Public Library (i) Shelv AR (b) Miami University Augmented Research Group (ii) Smart library (c) Oula University Library (iii) Wolf Walk (d) North Carolina State University (iv) Find the future Codes:
Which part of the QR code represents the encoded data?
