Consider a system of two non-interacting classical particles which can occupy any of the three energy levels with energy values E = 0, ε and 2ε having degeneracies g(E) = 1, 2 and 4 respectively, The mean energy of the system is
A. $$\varepsilon \left[ {\frac{{4\exp \left( {\frac{{ - \varepsilon }}{{{k_B}T}}} \right) + 8\exp \left( {\frac{{ - 2\varepsilon }}{{{k_B}T}}} \right)}}{{1 + 2\exp \left( {\frac{{ - \varepsilon }}{{{k_B}T}}} \right) + 4\exp \left( {\frac{{ - 2\varepsilon }}{{{k_B}T}}} \right)}}} \right]$$
B. $$\varepsilon \left[ {\frac{{2\exp \left( {\frac{{ - \varepsilon }}{{{k_B}T}}} \right) + 8\exp \left( {\frac{{ - 2\varepsilon }}{{{k_B}T}}} \right)}}{{1 + 2\exp \left( {\frac{{ - \varepsilon }}{{{k_B}T}}} \right) + 4\exp \left( {\frac{{ - 2\varepsilon }}{{{k_B}T}}} \right)}}} \right]$$
C. $$\varepsilon {\left[ {\frac{{2\exp \left( {\frac{{ - \varepsilon }}{{{k_B}T}}} \right) + 4\exp \left( {\frac{{ - 2\varepsilon }}{{{k_B}T}}} \right)}}{{1 + 2\exp \left( {\frac{{ - \varepsilon }}{{{k_B}T}}} \right) + 4\exp \left( {\frac{{ - 2\varepsilon }}{{{k_B}T}}} \right)}}} \right]^2}$$
D. $$\varepsilon \left[ {\frac{{\exp \left( {\frac{{ - \varepsilon }}{{{k_B}T}}} \right) + 2\exp \left( {\frac{{ - 2\varepsilon }}{{{k_B}T}}} \right)}}{{1 + \exp \left( {\frac{{ - \varepsilon }}{{{k_B}T}}} \right) + \exp \left( {\frac{{ - 2\varepsilon }}{{{k_B}T}}} \right)}}} \right]$$
Answer: Option D
Join The Discussion