So I have worked out the 'allowed' configurations for four particles which can occupy 5 different energy levels (1, 3, 5, 7, 9) and now I need to work out the average number of particles in a particular energy level (i.e 3).
1) 9,5,1,1
2) 9,3,3,1
3) 7,7,1,1
4) 7,3,3,3
5) 7,5,3,1
6) 5,5,5,1
7) 5,5,3,3
So there are 7 total configurations and three appears this number of times(in brackets):
1) 9,5,1,1 (0)
2) 9,3,3,1 (2)
3) 7,7,1,1 (0)
4) 7,3,3,3 (3)
5) 7,5,3,1 (1)
6) 5,5,5,1 (0)
7) 5,5,3,3 (2)
So would I say that 3 appears 8 times if all the sequences were counted to a total number of values of 28.
Am I on the right track or am I over complicating this?
I am thinking you missed the point. You have four particles, and each of them can be in energy level a,b,c,d,e
so you need to take those energy levels, choosing four at a time to get your possible combinations. You job is to find the average number of any letter.
a,a,a,b
a,a,b,a
a,b,a,a and so on (it is a long list). Seems a combination formula will get you the results quicker. Perhaps I am not understanding the problem.
Hi Bob,
Thanks for answering, I have gone the long way around with this question as im still not sure how I can end up with the average number of particles in N_3 can be 8/7.
But according to my textbooks the answer should be arrived at as follows:
<N_3>= (0*1/7)+(2*1/7)+(0*1/7)+(3*1/7)+(1*1/7)+(0*1/7)+(2*1/7)=8/7
You're on the right track! To calculate the average number of particles in a particular energy level, you need to count how many times that energy level appears in all the configurations and then divide it by the total number of configurations.
In your case, you correctly identified that the energy level 3 appears a total of 8 times in the 7 configurations. However, to calculate the average, you need to divide this number by the total number of configurations, which is 7. So the average number of particles in the energy level 3 would be 8/7.
It's important to note that the total number of values (28 in your case) doesn't come into play when calculating the average number of particles in a specific energy level. Instead, you focus on the count of the energy level in the configurations and divide it by the total number of configurations.