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The quantum concentration for room temperature protons is about 1/cubic-Angstrom.
As the quantum concentration depends on temperature, high temperatures will put most systems in the classical limit unless they have a very high density e.g. a White dwarf.
quantum, concentration, this, article, multiple, issues, please, help, improve, discuss, these, issues, talk, page, learn, when, remove, these, template, messages, this, article, relies, largely, entirely, single, source, relevant, discussion, found, talk, pag. This article has multiple issues Please help improve it or discuss these issues on the talk page Learn how and when to remove these template messages This article relies largely or entirely on a single source Relevant discussion may be found on the talk page Please help improve this article by introducing citations to additional sources Find sources Quantum concentration news newspapers books scholar JSTOR February 2013 This article includes a list of general references but it lacks sufficient corresponding inline citations Please help to improve this article by introducing more precise citations February 2013 Learn how and when to remove this message Learn how and when to remove this message The quantum concentration nQ is the particle concentration i e the number of particles per unit volume of a system where the interparticle distance is equal to the thermal de Broglie wavelength Quantum effects become appreciable when the particle concentration is greater than or equal to the quantum concentration which is defined as 1 n Q M k T 2 p ℏ 2 3 2 displaystyle n rm Q left frac MkT 2 pi hbar 2 right 3 2 where M is the mass of the particles in the system k is the Boltzmann constant T is the temperature as measured in kelvins ℏ displaystyle hbar is the reduced Planck constant The quantum concentration for room temperature protons is about 1 cubic Angstrom As the quantum concentration depends on temperature high temperatures will put most systems in the classical limit unless they have a very high density e g a White dwarf For an ideal gas the Sackur Tetrode equation can be written in terms of the quantum concentration as 1 S T V N N k B 5 2 ln n Q n displaystyle S T V N Nk rm B left frac 5 2 ln left frac n rm Q n right right References edit a b Charles Kittel Herbert Kroemer 1980 Thermal Physics 2 ed W H Freeman pp 73 77 ISBN 978 0716710882 nbsp This quantum mechanics related article is a stub You can help Wikipedia by expanding it vte nbsp This article about statistical mechanics is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Quantum concentration amp oldid 1100222255, wikipedia, wiki, book, books, library,
