Question

2. Fermi-Dirac Statistics. Verify for both the Fermi-Dirac and Bose-Einstein grand partition functions Ż (Equations 7.21 and 7.24 respectively) that the occupancies D (Equation 7.23) and BE (Equation 7.28) can be computed by -1 až where h kT 7.2 Bosons and Fermions called the Fermi-Dirac distribution; I'll call it TFD (7.23) FDT ibution goes to zero when u, and goes to 1 when energy much less than u tend to be occupied, while states r than u tend to be unoccupied. A state with energy 50% chance of being occupied, while the width of the w times kT. A graph of the Fermi-Dirac distribution vs. is shown in Figure 7.6. eratures es in question are bosons, then n can be any nonn tition function is (7.27) 1 (bosons). BE ula is called the Bose-Einstein distribution: I'll call it (7.28) Dirac distribution, the Bose-Einstein distribution goes to zero e the Fermi-Dirac distribution, however, it goes to infinity ase above (see Figure 7.7). It would be negative if e could be less lready seen that this cannot happen. stand the Fermi-Dirac and Bose-Einstein distributions, it's use- ould be for particles obeying Boltzmann statistics. In this case, amy snge particle being in a certain state of energy c is P(s)e-e/kT

Answer 1

Partition uncthion fon Bosong Sum our microstate Cm;

taking natunal now se 22. sEr eY BE にe-PCS-dl) BE kて

Ani CE;-서 ) + 1
first calculate the partition function for BE and FD then use given relation ....