Question

3 particles with a unit energy of 5.

Find the total # of macrostates.

Find the # of microstates for each macrostate.

Answer 1

The total energy of 5 units is distributed among 3 particles

so, the macrostates will be like:

(0,0,5) or (1,2,2) or (3,2,0) or (4,1,0)

therefore, the number of macrostates is 4.

If the particles are INDISTINGUISHABLE, for the macrostate (0,0,5) there is only 1 microstate

(0,0,5) = (0,5,0) = (5,0,0)

number of microstates for (1,2,2) is 3

[they are (2,1,2), (1,2,2) and (2,2,1)]

number of microstates for (3,2,0) is 6 with the states being (3,2,0) , ( 0,2,3) , (3,0,2) , (2,0,3), (2,3,0) and (0,3,2).

number of microstates for (4,1,0) is 6 with the states being (4,1,0) , (4,0,1) , (0,1,4) , (0,4,1), (1,4,0) and (1,0,4).