Entropy of a quantum sized material

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SUMMARY

The discussion focuses on calculating the entropy of a quantum-sized material with energy levels spaced 2E-23 J apart and a total energy of 34E-23 J, containing 5 atoms. The key equations involved are the entropy formula, Entropy = (Boltzmann's constant) * ln(multiplicity), and the multiplicity formula, Multiplicity = (q + N - 1)!/[q!(N-1)!]. The user attempted to determine the value of N, concluding it to be 18, but faced challenges in applying the multiplicity equation correctly to derive the entropy. The correct approach to finding N and using the multiplicity equation is essential for accurate entropy calculation.

PREREQUISITES
  • Understanding of Boltzmann's constant and its role in entropy calculations
  • Familiarity with the concept of multiplicity in statistical mechanics
  • Basic knowledge of quantum mechanics and energy quantization
  • Ability to perform factorial calculations and logarithmic functions
NEXT STEPS
  • Review the derivation of Boltzmann's entropy formula and its applications
  • Study the concept of multiplicity in statistical mechanics in detail
  • Learn how to calculate energy levels in quantum systems
  • Explore examples of entropy calculations for different quantum systems
USEFUL FOR

Students and researchers in physics, particularly those studying statistical mechanics and quantum thermodynamics, will benefit from this discussion. It is also relevant for anyone involved in entropy calculations in quantum systems.

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Homework Statement


A small material has quantum oscillator energy levels 2E-23 J apart. Suppose the material has a total energy of 34E-23 J and contains 5 atoms. Find the entropy of the material.


Homework Equations


Entropy = (Boltzmann's constant)*ln(multiplicity)

Multiplicity = (q + N - 1)!/[q!(N-1)!]


The Attempt at a Solution


I'm having trouble grasping the question. The 5 atoms are understood, but I'm having trouble finding the "N" for the multiplicity equation.

So, I came up with N = 18, because the total energy is 34E-23 J and the energy levels are 2E-23 J apart, and q = 5.

Then applying the multiplicity equation and plugging it to entropy, I didn't get the correct answer.

Am I on the correct path to find N, or do I even need the multiplicity equation?
 
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