A system of independent particles (energy levels)

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The discussion revolves around the application of the Boltzmann Distribution to determine the temperature at which 20% of independent particles occupy a higher energy level (ε1 = 50 meV) in a two-level system. Participants clarify that the variable z refers to the partition function, which is crucial for the calculation. The user seeks confirmation on their calculations and understanding of the relevant equations. The hint provided includes constants for temperature calculations, emphasizing the need for accurate application of these values. Overall, the thread focuses on resolving uncertainties regarding the correct use of the Boltzmann Distribution in this context.
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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