A system has two normal modes of vibration, with frequencies @, and @₂ = 2w₁ . What is the probability that at temperature T, the system has an energy less than 4ħw, ? [In the following x = e-hand Z is the partition function of the system.] 3/2 (a) x³/²(x+2x²)/ Z (b) x³/² (1+x+x²) / Z 3/2 3/2 (c) x ³/² (1+2x²)/Z (d) x³/² (1+x+2x²)/Z
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