How Do Macrostates and Microstates Determine Particle Energy Distribution?

[pinkfishegg]

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

 

[haruspex]

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.

 

[pinkfishegg]

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

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]

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.

 

[collinsmark]

@pinkfishegg,

You mentioned that the answer is in the back of the book. Out of curiosity, what is the given answer?

 

[pinkfishegg]

@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%