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A system of non-interacting fermi particles with fermi energy εf has the density of states proportional to √ε where ε is the energy of the particle. Then the average energy per particle at temperature T = 0 K is
  • a)
    1/6 εf
  • b)
    1/5 εf
  • c)
    2/5 εf
  • d)
    3/5 εf
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A system of non-interacting fermi particles with fermi energy &epsilon...
n(ε) dε =  
At T = 0 K, all non-integrating particles have energy < εr
So, 
NOW, 
So, 
Then average energy per particle at T = 0 K.
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Most Upvoted Answer
A system of non-interacting fermi particles with fermi energy &epsilon...
n(ε) dε =  
At T = 0 K, all non-integrating particles have energy < εr
So, 
NOW, 
So, 
Then average energy per particle at T = 0 K.
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Community Answer
A system of non-interacting fermi particles with fermi energy &epsilon...
Density of States Function
- Given that the density of states is proportional to √ε, we have g(ε) = A√ε, where A is a constant.

Fermi Energy
- Fermi energy εf corresponds to the highest occupied energy level at T = 0 K.

Average Energy per Particle
- The average energy per particle at T = 0 K can be calculated by integrating the energy over the density of states up to the Fermi energy.
- The average energy per particle is given by:
E_avg = ∫(0 to εf) &epsilon*g(ε) dε / ∫(0 to εf) g(ε) dε
E_avg = A∫(0 to εf) ε√ε dε / A∫(0 to εf) √ε dε
E_avg = ∫(0 to εf) ε√ε dε / ∫(0 to εf) √ε dε
E_avg = [2/5 * εf^5/2] / [2/3 * εf^3/2]
E_avg = 3/5 * εf
Therefore, the average energy per particle at T = 0 K is 3/5 * εf, which corresponds to option 'D'.
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