Using the derived partition function for a single harmonic oscillator in three different directions provided above, show that the partition function for a crystal of n atoms is given by For 3D the partition function will beZ3DZ³=exp{-(hu)KBThw1- exp{-KBTwhich is the partition function for the 3D harmonic oscillator.Z3D =Q sysZ³=3. Using your answer to part (2), show that the partition function for a crystal of n atoms (i.e., a collection ofharmonic oscillators in three different directions) is given by:3Nexp(-Bhv)1-exp(-Bhv)

Since for single particle the partition function is given.

Answered: For 3D the partition function will be…

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