Consider a system with two energy levels (orbitals) with energies 0 and e. The system is in contact with a heat reservoir at temperature T = 1/(kB), with T chosen so that e-B = 1/2. It is also in contact with a particle reservoir, whose chemical potential is chosen so that the mean number of particles in the system is 1. [Warning: do not assume that the number of particles in the system is always 1. This is only the mean number of particles. In part (b) this distinction is crucial to getting the right answer.] (a) Assuming the particles obey classical (Maxwell-Boltzmann) statistics, find the mean numbers of particles no and ñ, in the states with energy 0 and €, respectively. (b) Repeat part (a) assuming the particles obey Bose-Einstein statistics. The quadratic equation you have to solve to get the answer of course has two roots. Explain clearly,

Consider a system with two energy levels (orbitals) with energies 0 and e. The system is in contact with a heat reservoir at temperature T = 1/(kB), with T chosen so that e-B = 1/2. It is also in contact with a particle reservoir, whose chemical potential is chosen so that the mean number of particles in the system is 1. [Warning: do not assume that the number of particles in the system is always 1. This is only the mean number of particles. In part (b) this distinction is crucial to getting the right answer.] (a) Assuming the particles obey classical (Maxwell-Boltzmann) statistics, find the mean numbers of particles no and ñ, in the states with energy 0 and €, respectively. (b) Repeat part (a) assuming the particles obey Bose-Einstein statistics. The quadratic equation you have to solve to get the answer of course has two roots. Explain clearly,