For a system of two identical particleswith spin I the ratio of number ofstates which are symmetric under spininterchange to the number of stateswhich are antisymmetric under spininterchange isงา

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The ratio of the number of states symmetric under spin interchange to the number of states…

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View a system of two particles that do not interact with each other, where each particle can occupy three possible states, each with energy &, 2ɛ, 3E (i) Marwell-Boltzmann: Na. Configuration 1 2 3 4 S 6 7 2 9 Nader Conligation 1 2 2 + 1 2 5 6 (1) Fermi-Dirac 3 No. Configuration E AG A A B B AA A A Distinguishable 28 E AB (6) Boson: Base- Ginstein: Indistinguishable င် A A B A A 8 28 AA A A 38 A 2 A AB B A CO B A JE AA A A Energy system A A wwwww Indistinguishable We know formion follow exclusion principle. 28 38 Smarty tem 28 32 38 4E SE SE Energy system 22 48 68 38 48 SE 38 4€ SE Calculate the average energy of the system as a temperature function for the three statistics above.
8. Curie susceptibility: consider N non-interacting quantized spins in a magnetic field B = Bê, and at a temperature T. The work done by the field is given by BM,, with a magnetization M, = µ, m,. For each spin, m, takes only the 2s+1 values -s, -s+ 1,...,s-1, s. (a) Calculate the Gibbs partition function 2(T, B). (Note that the ensemble corresponding to the macrostate (T, B) includes magnetic work.) (b) Calculate the Gibbs free energy G(T, B), and show that for small B, Nµ²s(s+1)B² 6k gT G(B) = G(0) – +0(B*). %3D (c) Calculate the zero field susceptibility x = JM,/ƏB|-0, and show that it satisfies %3D B=0+ Curie's law X=c/T. (d) Show that Cg-CM = cB?/T², where Cg and CM are heat capacities at constant B and M, respectively.
4. If a kind of particles obeys the following dispersion -Dpa, what is the density of states (three dimensions)?
A 10 monolayers thick layer of Ag is deposited on Mo. The intensity of electrons emitted by the Ag and Mo can be measured separately. The ratio IAg/IMoi =100 for the deposited film. The mean free path of the electrons is 0.6 nm and the thickness of one layer is 0.18 nm. After heating the sample, the Ag layer has agglomerated in islands that cover a fraction q of the surface. Between the islands the Mo is “visible”. The intensity ratio after agglomeration is IAg/IMof = 1. Calculate the sensitivity of the electron spectroscopy technique for Ag with respect to Mo. I.e. how many electrons are emitted from one layer of Ag atoms compared to one layer of Mo atoms. And use this to determine what fraction of the surface is covered by islands?

For a system of two identical particles with spin I the ratio of number of states which are symmetric under spin interchange to the number of states which are antisymmetric under spin interchange is งา