# Homework Help: Macrostates and microstates

1. Oct 10, 2015

### pinkfishegg

1. The problem statement, all variables and given/known data
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?

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

3. 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 im 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

2. Oct 11, 2015

### haruspex

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.

3. Oct 11, 2015

### pinkfishegg

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

4. Oct 11, 2015

### haruspex

That's my guess.

5. Oct 11, 2015

### collinsmark

@pinkfishegg,

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

6. Oct 11, 2015

1)3
2)3,6,1
3) 20%, 40%