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Chemistry · Glossary

What is Microstate, statistical weight?

Also known as: microstate · statistical weight

Definition 10.1 University Chemistry — Year 3 · Chapter 10 — Statistical Thermodynamics: Partition Functions

A microstate of a system of molecules is a complete specification of the state of every molecule. The statistical weight WW of a distribution {ni}\{n_i\} of NN molecules over non-degenerate levels is the number of microstates that realise it:

W=N!n0! n1! n2!⋯.W = \frac{N!}{n_0!\,n_1!\,n_2!\cdots}.

Examples

Example 10.2 (Three quanta among three oscillators)

Three oscillators share three quanta of energy. The distribution “one oscillator holds all three” can be realised in 3!/(1! 2!)=33!/(1!\,2!) = 3 ways, “one holds two, another one” in 3!=63! = 6 ways and “each holds one” in one way: ten microstates in all, and the most even distribution that still spreads the energy over several levels is the most probable. With 102310^{23} molecules the weights become so sharply peaked that one distribution, and the ones that differ from it by a negligible amount, carry practically all the microstates.

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