The Schottky Anomaly Schottky\'s anomaly refers to the characteristic \"bump\" i

Question

The Schottky Anomaly Schottky's anomaly refers to the characteristic "bump" in the heat capacity graph of any two-level quantum system. Schottky's theorem says that for any two-state system with energy gap omega between the upper and lower states, the heat capacity exhibits a maximum value of 0.44k at T = 0.42omega/k. Consider a two-state system (energy gap omega) in thermal equilibrium with a reservoir (temperature T).Calculate the heat capacity C of the system (at constant Omega) as a function of T. Make an accurate graph of C/k versus kT/Omega. Does your graph prove Schottky's theorem Explain. Schottky's theorem provides a useful thermodynamic tool to measure atomic fine structure. Suppose you measure the heat capacity of a new material and detect a Schottky bump at 37.4 mK. You conclude that the atoms in this material have a pair of closely-spaced energy levels. What is the frequency of electromagnetic radiation associated with this thermodynamic bump

Explanation / Answer

a) At low temperature C= T3

at high temperature Cv = 3R (where C stand for specific heat at constant voloume)

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