Small oscillations

A system of two atoms can be in three quantum states having energies 0, € and Z€. The system is in equilibrium at temperature T = (kвB)-1 . Match the following Statistics with the Partition function. Statistics Partition function CD: Classical (distinguishable particles) 71: e-BE + e 2B€ + e 3߀ CI: Classical (indistinguishable particles) 72: 1 + e-BE + 2e-2ßE + e-3ßE + e 4ßE FD: Fermi-Dirac Z3: 1 + Ze-BE + 3e-2ßE + Ze-3߀ + e-4ßE BE: Bose-Einstein (A) (B) (C) (D) CD:Z1, CI: Z2, FD:Z3, BE:Z4 CD:Z2, CI:Z3, FD:ZA, BE:Z1 CD:23, CIZA, FD: 21, BE: 22 CD:ZA, CI:Z1, FD:Z2, BE:Z3

Options:

• (A)
• (B)
• (C)
• (D) CD:Z1, CI: Z2, FD:Z3, BE:Z4 CD:Z2, CI:Z3, FD:ZA, BE:Z1 CD:23, CIZA, FD: 21, BE: 22 CD:ZA, CI:Z1, FD:Z2, BE:Z3