How Do Macrostates and Microstates Determine Particle Energy Distribution?

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The discussion revolves around the concepts of macrostates and microstates in the context of three non-interacting particles sharing three units of energy. It clarifies that there are three distinct macrostates based on different energy distributions, and the number of microstates varies for each macrostate, with calculations suggesting 3 microstates for one distribution and 6 for another. The probability of finding one particle with 2 units of energy is estimated at 1/6, while the chance of a particle having 0 units of energy is considered to be 1/3. Participants express confusion over the definitions and calculations, emphasizing that macrostates represent energy distributions and microstates represent arrangements of these distributions. The thread concludes with reference to the answers provided in the textbook.
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Homework Statement


A collection of three non-interacting particles shares 3 units of energy. Each particle is restricted to having an integral number of units of energy.
a)How many macrostates are there?
b)How many microstates are there in each of the macrostates?
c)What is the probability of finding one of the particles with 2 units of energy? With 0 units of energy?[/B]

Homework Equations


Definitions:
macrostate: each possible energy distribution
microstate: the various arrangement of microstates according to a given macrostate

The Attempt at a Solution



The answers are in the back of the book but I'm not really clear on the concepts

a) There are 3 macrostates because there are 3 units of energy?
b) My first though was that you could have either:
3 microstates in each macrostate There are 3 ways to do that
2 microstates in one microstate, 1 in anouther. There are 6 ways to do this
2 microstates per macrostate

c) if what I am saying is right than there's a 1/6 chance that one particle has 2 units of energy, and a 1/3 chance they have zero units of energy
 
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pinkfishegg said:
Definitions:
macrostate: each possible energy distribution
That's not a crystal clear definition, but I think perhaps it means the different ways the energy can be distributed if you consider the particles as interchangeable. E.g. 0,1,2 is the same as 1,2,0 etc.
I certainly don't think the number of macrostates is merely the number of energy units in total.
The number of microstates will be different for each macrostate.
 
haruspex said:
That's not a crystal clear definition, but I think perhaps it means the different ways the energy can be distributed if you consider the particles as interchangeable. E.g. 0,1,2 is the same as 1,2,0 etc.

So the the energy units can be distrubuted

3 macrostates=3 combination of different units
3-0-0 0-3-0 0-0-3 2-1-0 2-0-1 1-2-0 1-0-2 0-1-2 0-2-1 1-1-1
3 microstates 6 microstates 1 microstate

haruspex said:
I certainly don't think the number of macrostates is merely the number of energy units in total.
The number of microstates will be different for each macrostate
 
pinkfishegg said:
So the the energy units can be distrubuted

3 macrostates=3 combination of different units
3-0-0 0-3-0 0-0-3 2-1-0 2-0-1 1-2-0 1-0-2 0-1-2 0-2-1 1-1-1
3 microstates 6 microstates 1 microstate
That's my guess.
 
@pinkfishegg,

You mentioned that the answer is in the back of the book. Out of curiosity, what is the given answer?
 
collinsmark said:
@pinkfishegg,

You mentioned that the answer is in the back of the book. Out of curiosity, what is the given answer?
1)3
2)3,6,1
3) 20%, 40%
 
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