Macrostates of 6 F-D particles? (Answer key wrong?)

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In summary, macrostates refer to the overall properties of a system, while microstates refer to the specific configurations of particles within that system. For F-D particles, macrostates are described by the number of particles in a particular energy level, and microstates refer to the arrangement of those particles in that energy level. According to F-D statistics, the number of microstates for a given macrostate is equal to the binomial coefficient (n choose k), where n is the total number of particles and k is the number of particles in the desired energy level. The number of microstates cannot exceed the number of particles in the system, as each particle can only occupy one energy level at a time. The number of available energy levels directly affects the
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Homework Statement



For six indistinguishable particles obeyed Fermi Dirac statistics where multiplicity, Ω = 162, g = 3 (degeneracy), U = 7
a. Find the total number of macro states.
Answer in book: 8. Idk why
b. Calculate the thermodynamic probability, W of each macro state.
d. Find the average occupation number of each state
Answer: 2.27,1.722,1.056,0.667,0.0222,0.056
BOOK MIGHT BE WRONG.

Homework Equations


W = ∏(over j) gj! / (gj-Nj)!Nj!
<Nj> = Ω^-1 * ∑(over k) NjkWk

The Attempt at a Solution


I drew out 6 macro states.
I got thermo prob of 9, 27, 9,81,9,9 and the occupation numbers didn't match up.
 
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SOLVED. Made mistake in drawing of macro states.
 

FAQ: Macrostates of 6 F-D particles? (Answer key wrong?)

1. What are macrostates and microstates in the context of F-D particles?

Macrostates refer to the overall properties of a system, such as its energy or volume, while microstates refer to the specific configurations of individual particles within the system. In the case of F-D particles, macrostates can be described by the number of particles in a particular energy level, while microstates refer to the specific arrangement of these particles in that energy level.

2. How is the number of microstates related to the number of particles in a macrostate?

According to the F-D statistics, the number of microstates for a given macrostate is equal to the number of ways the particles can be distributed among the available energy levels. This number is given by the binomial coefficient (n choose k), where n is the total number of particles and k is the number of particles in the desired energy level.

3. Can the number of microstates for a given macrostate be greater than the number of particles?

No, the number of microstates for a given macrostate cannot exceed the number of particles. This is because each particle can only occupy one energy level at a time, and thus there can only be as many microstates as there are particles in the system.

4. How does the number of available energy levels affect the number of microstates?

The number of available energy levels has a direct impact on the number of microstates. As the number of energy levels increases, the number of microstates also increases, leading to a larger number of possible configurations for the particles. This is known as the "degeneracy" of the system.

5. Is there a limit to the number of microstates for a given macrostate?

Yes, there is a limit to the number of microstates for a given macrostate. This limit is given by the total number of particles in the system, as each particle can only occupy one energy level at a time. Therefore, the maximum number of microstates is equal to the total number of particles in the system.

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