(b)(i) Gas particles are composed of Fermions, which have non-integer spin states and must obey pauli-exclusion principles. This, these particles cannot occupy the same set of quantum numbers. This reduces the probability that these particles would exist in identical quantum states.
Bosons have integer spin states, and do not obey pauli-exclusion principles. In other words, they can occupy the same set of quantum numbers. Bosons therefore, are much more likely to be found in the same quantum state than are fermions
A hypothetical gas consists of four indistinguishable particles. Each particle may sit in one of five allowed quantum states, with energies ε,3ε,5ε,7ε and 9ε. Assume that the total energy of the gas is fixed at 16ε.
(a) If the particles are bosons: .
(i) What is the probability of finding two or more particles in the state of energy 3ε?
(ii) What is the average number of particles in the state of energy 3ε?
(b) If the particles are fermions:
(i) What is the probability of finding two or more particles in the state of energy 3ε?
(ii) What is the average number of particles in the state of energy 3ε?
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