Boltzmann’s distribution law

Apart from depending on the numerical value of the square of the transition moment of Equation (5.13), which varies relatively little with J, intensities depend on the population of the lower state of a transition. The population A/ of the Jth level relative to Aq is obtained from Boltzmann s distribution law. Equation (2.11) gives... 

Guggenheim, E. A., Boltzmann s Distribution Law, North-Holland, Amsterdam, Interscience, New York, 1955, pp. 47, 48. 

The first effect is that of a concentration change of the charged reactant particles in the reaction zone this change is determined by Boltzmann s distribution law ... 

See also Boltzmann s Distribution Law and Boltzmann Transport Equation. 

This fundamental relation is called Boltzmann s distribution law after the creator of statistical mechanics, Ludwig Boltzmann (1844-1906), Professor of Physics in Leipzig, and k is called Boltzmann s constant. 

In conclusion we must mention that a necessary condition for the validity of Eq, (3), and consequently of other formulas derived from Eq. (3) is that Ni < 1 for the state (or states) of lowest energy and a fortiori for all other states, When this inequality does not hold. Boltzmann s distribution law must be replaced by a more general and more precise distribution law, either that of Fermi and Dirac or that of Bose and Einstein according to the nature of the molecules. See also Statistical Mechanics. 

In our discussion of the kinetic theory of gases we have already shown that a statistical argument gives Boltzmann s distribution law for the probability of a definite energy state, according to which a definite state with energy E has the probability... 

To enable us to discuss the electrostatics of electrolyte solutions we need to introduce another fundamental principle - Boltzmann s distribution law — which relates the probability of particles being at a given point at which they have a potential energy, or free energy, A G, relative to some chosen reference state. This probability may be expressed in terms of the average concentration, c, at the point considered relative to that, r", at the reference level, taken as the zero of energy. If the temperature is T, then... 

As the examples above have shown, the mass action and excitation equations = + RT]n c/c ) and yS (w) = jS (0) - - w/t together accomplish what Boltzmann s distribution law does. When put together, they seem to represent a special version of this law that is closer to chemistry. We obtain the usual form if we interpret the concentration c(w) of the particle of type B(w) as a measure of the probability p w) of encountering the B particles in a state with energy w. 

The total number of atoms A with translational energy between w and w- -dwi then given, according to Boltzmann s distribution law, by... 

Guggenheim s Boltzmann s Distribution Law treats the subject of the title in its widest aspects. The factorization of the partition function is discussed and equations are given for the partition function for some simple degrees of freedom. The results are used to outline the properties of ideal monatomic gases, and in later sections free energy, total energy. 

By Boltzmann s distribution law the probability that a segment makes an angle 6 with the x-axis is proportional to ... 

Classical statistical mechanics state that Boltzmann s distribution law applies to a single closed system held at a fixed temperature, and populating different energy levels. In contrast, the database of known protein structures is a collection of minimum-energy conformations belonging to distinct proteins, the structural components of which occur in quite different environments. 

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