Please show all working. 1. Consider a model thermodynamic assembly in which the allowed one-particle states have energies 0, ɛ, 2ɛ, 3ɛ, 4ɛ, 5ɛ, 6ɛ,. The assembly has four particles and a total energy of 6ɛ. Identify the possible particle number distributions and calculate the average distribution of the three particles in the energy states when the particles are (a) localized and distinguishable (b) gaseous bosons (c) gaseous fermions

Please show all working. 1. Consider a model thermodynamic assembly in which the allowed one-particle states have energies 0, ɛ, 2ɛ, 3ɛ, 4ɛ, 5ɛ, 6ɛ,. The assembly has four particles and a total energy of 6ɛ. Identify the possible particle number distributions and calculate the average distribution of the three particles in the energy states when the particles are (a) localized and distinguishable (b) gaseous bosons (c) gaseous fermions

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Please show all working. 1. A linear lattice with lattice constant a has a basis of two identical atoms of mass m where the equilibrium spacing of the atoms within each unit cell is b (where b <5. The displacements of the atoms from their equilibrium positions are given by u,U2, ---, Uzn-1,Uzn, Uzn+1, -.. The harmonic forces between nearest-neighbour atoms are characterised by the alternating interatomic force constants B, and B.. (a) Develop: (i) The equation of motion for the 2nth atom in terms of forces exerted by the (2n - 1)th and (2n + 1)*th atoms. (u) The equation of motion for the (2n + 1)th atom in terms of forces exerted by the 2nth and (2n + 2)th atoms. (b) Using the equations of motion and assuming travelling wave solutions of the form Un = Aet-kna) and Um = Bei(@t-kna-kb) derive two simultaneous equations for A and B. (c) Making use of the fact that a homogeneous system of linear equations C11x + C2y = 0 C2,x + Cy = 0 only has a non-zero solution for x and y when C12 =0.…
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