Bose-Einstein Statistics: Finding W.

[atomicpedals]

Homework Statement

Given 4 particles to be divided among 2 zones, one of 3 cells and one of 2 cells. For B-E statistics find W for each macrostate from N₁=4, N₂=0 to N₁=0, N₂=4, using both the formula and block diagram.

Homework Equations

The relevant equation is W=(g+N_i-1)!/(g-1)!N_i!

The Attempt at a Solution

There are, I believe, five W's to be found. I've found the first one fairly quickly; W=6!/2!4!=15, and I think I found the fifth one as well, W=5!/1!4!=5. However the possible results in between seem to escape me even though it should be fairly trivial! Am I approaching the problem correctly?

 

[mark726]

Thank you for your post. It seems like you are on the right track with finding the first and fifth W values. However, there are actually six W values to be found, as there are six different macrostates from N1=4, N2=0 to N1=0, N2=4.

To find the remaining W values, you can use the same formula you used for the first and fifth values, but with different values for g and Ni. For example, for the second macrostate (N1=3, N2=1), the formula would be W=(g+Ni-1)!/(g-1)!Ni!= 5!/2!3!=10.

Alternatively, you can also use a block diagram to visualize the different ways the particles can be distributed among the two zones. This can help you to see all the possible combinations and calculate the corresponding W values.

I hope this helps. Good luck with your calculations!



Scientist