A system of independent particles (energy levels)

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SUMMARY

The discussion centers on calculating the temperature at which 20% of independent particles occupy an energy level of ε1 = 50 meV using the Boltzmann Distribution. The partition function, denoted as z, is crucial for this calculation. The relevant constants provided are k = 1.38E-23 J/K and e = 1.60E-19 As. Participants emphasize the importance of correctly applying the Boltzmann Distribution formula and understanding the role of the partition function in determining the distribution of particles across energy levels.

PREREQUISITES
  • Understanding of the Boltzmann Distribution
  • Knowledge of energy levels in statistical mechanics
  • Familiarity with partition functions in thermodynamics
  • Basic concepts of degeneracy in quantum mechanics
NEXT STEPS
  • Study the derivation and application of the Boltzmann Distribution
  • Learn how to calculate the partition function for systems with multiple energy levels
  • Explore the implications of degeneracy on particle distribution
  • Investigate temperature dependence of energy distributions in statistical mechanics
USEFUL FOR

Students and professionals in physics, particularly those focusing on statistical mechanics, thermodynamics, and quantum mechanics, will benefit from this discussion.

physicisttobe
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Homework Statement
boltzmann distribution
Relevant Equations
…
Hi guys,

Can you give me some feedback on whether my calculation is correct? I applied the formula below (Boltzmann Distribution) but I didn‘t know what to use for the variable z. I don‘t even know if I used the correct equation. Can you help me further?

The task is:
Consider a system of independent particles that can only occupy 2 different energy levels ε0 = 0 (non-degenerate) or ε1 = 50 meV (3-fold degenerate). At what temperature do 20% of the particles have energy ε1?

Hint: k= 1.38E-23 J/K
e= 1.60E-19 As

B3EF1F20-B87A-4A41-AB44-DF8121B70346.jpeg
 
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physicisttobe said:
Homework Statement: boltzmann distribution
Relevant Equations: …

Hi guys,

Can you give me some feedback on whether my calculation is correct? I applied the formula below (Boltzmann Distribution) but I didn‘t know what to use for the variable z. I don‘t even know if I used the correct equation. Can you help me further?

The task is:
Consider a system of independent particles that can only occupy 2 different energy levels ε0 = 0 (non-degenerate) or ε1 = 50 meV (3-fold degenerate). At what temperature do 20% of the particles have energy ε1?

Hint: k= 1.38E-23 J/K
e= 1.60E-19 As

View attachment 325293
z is not a variable. It's the partition function.
 

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