# A system of independent particles (energy levels)

• physicisttobe
The correct equation to use is e^(-ε1/kT)=0.2. In summary, the conversation is about calculating the temperature at which 20% of independent particles in a system have energy level ε1 using the Boltzmann Distribution formula and the given hint. The correct equation to use is e^(-ε1/kT)=0.2 and z is the partition function.
physicisttobe
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?

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

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?

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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