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Consider the possible states that N particles can occupy if there are only three possible energy levels whose degeneracy is one. N1 is the number of particles occupying level 1; N2, level 2; N3, level 3. Therefore N = N1 + N2 + N3. Also, the total energy, E = N1 ?1+ N2 ?2 + N3 ?3. Let the energies of the three levels be (in arbitrary units): ?1 = 0; ?2 = 1; ?3 = 3. Let N = 20,000 and let E = 10,000. The expressions for N and E give us two equations in three unknowns: N1, N2, and N3. a. Take N3 as the independent variable and solve for N2 in terms of N3. Then solve for N1 in terms of N2 and N3. b. Taking note that there cannot be a negative population, what are the possible values of N3 ?
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