Fermi-Dirac Distribution

In summary, the conversation discusses the calculation of the probability of a copper energy state being populated at a certain temperature using the fermi-Dirac distribution formula. The calculated temperature did not seem to be the correct answer, leading to a discussion on the distribution function and its relationship to probability.
  • #1
viviane363
17
0
Pleas can you help me figure out what I do wrong?
At what temperature is the probability that an energy state at 7.00 eV will be populated equal to 25 percent for copper (EF = 6.95 eV)?
The formula for the fermi-Dirac Distribution is f(E) = 1/(1+e^((E-EF)/kT)) and looking at the problem I figured that f(E) = 25%=0.25 and E-EF=7.00 - 6.95 = 0.05eV
solving for T and found that T=3.2979e21 K, but it doesn't seem to be the right answer, why?
 
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  • #2
I think this thread should be move to the homework forum.
Anyway, f(E) is DISTRIBUTION function; not a probability so setting f(E)=0.25 doesn't make sense.

Consider this: How would you calculate the probability that the system is in ANY state?
You already know that this probability is one, but in problems like this it neverthless help to write down the expression.
 
  • #3


It seems like you have correctly applied the formula for the Fermi-Dirac distribution to solve for the temperature at which the probability of an energy state at 7.00 eV being populated is equal to 25%. However, the answer you have obtained, 3.2979e21 K, seems to be unrealistic. This could be due to a few possible reasons:

1. Units: Make sure that all the units in your calculation are consistent. The value of 7.00 eV should be converted to joules (J) before plugging it into the formula, as the units for temperature are in kelvin (K) and energy in joules (J).

2. Calculation error: Double-check your calculations to make sure there are no errors. It's always a good idea to double-check your work, especially when dealing with complex equations.

3. Assumptions: The Fermi-Dirac distribution assumes that the system is in thermal equilibrium, and there are no external factors affecting the distribution of particles. If this assumption is not met, it could lead to unrealistic results.

I would recommend going through your calculations again and checking for any possible errors. If you are still getting an unrealistic answer, it might be helpful to consult with a colleague or a mentor for further assistance.
 

1. What is the Fermi-Dirac Distribution?

The Fermi-Dirac Distribution is a probability distribution function that describes the distribution of fermions (particles with half-integer spin) in a system at thermal equilibrium. It was developed by Enrico Fermi and Paul Dirac in the 1920s to explain the behavior of electrons in a metal.

2. How is the Fermi-Dirac Distribution different from other probability distributions?

The Fermi-Dirac Distribution is unique in that it takes into account the Pauli exclusion principle, which states that no two fermions can occupy the same quantum state. This results in a distribution that is characterized by a sharp cutoff at a certain energy level, known as the Fermi energy.

3. What is the significance of the Fermi energy in the Fermi-Dirac Distribution?

The Fermi energy is a key parameter in the Fermi-Dirac Distribution as it represents the energy level at which the probability of finding a fermion is 0.5. This energy level also determines the behavior of fermions in a system, such as their electrical and thermal conductivity.

4. How is the Fermi-Dirac Distribution used in physics?

The Fermi-Dirac Distribution is used in many areas of physics, such as condensed matter physics, quantum mechanics, and statistical mechanics. It is particularly important in understanding the behavior of electrons in materials, such as metals, semiconductors, and insulators.

5. Can the Fermi-Dirac Distribution be applied to other particles besides electrons?

Yes, the Fermi-Dirac Distribution can be applied to any type of fermion, such as protons, neutrons, and quarks. It can also be extended to describe the behavior of bosons (particles with integer spin) by using the Bose-Einstein statistics instead of the Fermi-Dirac statistics.

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