Question

2.A single particle has energy levels 0, ?,-?, 2 ?, and-2? a) Write the single particle partition function, z. b) Write the canonical partition function, Z, for an c) Write the probability P, for the particle to have d) At T-0.1 &/kB, calculate P, for the particle to have e) Calculate the average energy of an assembly of N assembly of N such particles. energy 0, e,-?,2?, or-2e. energy of 0 and e. particles at very high temperatures

Answer 1

The partition function is, z = Sigma e^- beta H = Sigma e^- beta elementof where beta = (k_B T)^- 1 Therefore = 1 + e^- beta elementof + e^beta elementof + e^- beta(2 elementof) + e^beta(2 elementof) = 1 + 2 cosh beta elementof + 2 cosh 2 beta elementof is the single particle partition function for N-particle Z_N = Z^N = (1 + 2 cosh beta elementof + 2 cosh 2 beta elementof)^N p_0 = 1/1 + 2 cosh beta elementof + 2 cosh e beta elementof + elementof is, p_+ elementof = e^- beta elementof/1 + 2 cosh beta elementof + 2 cosh 2 beta elementof + 2 elementof is, p_+ 2 elementof = e^- 2 beta elementof/1 + 2 cosh beta elementof + 2 cosh 2 beta elementof - 2 elementof is, p_-2 elementof = e^2 beta elementof/1 + 2 cosh beta elementof + 2 cosh 2 beta elementof particle having energy