Einstein solid and the width of Gaussians

[Niles]

Homework Statement

If I have two Einstein solids A and B with oscillators N_A N_B and they share a total of 20 energy units.

I want to find the width of the function that describes the multiplicity for this system. How do I find this?

- I have an expression in my book (Thermal Physics by Schroeder), where the width is given as q/sqrt(N), where q is the energy units and N is the number of oscilators of one of the systems A and B - but in that example, A and B have the same number of oscillators N. I was just wondering how it is when they have a different amount.

 

[Jhero]

Thank you for your question. The width of the function describing the multiplicity for a system of two Einstein solids with different numbers of oscillators can still be calculated using the same expression you mentioned from your textbook: q/sqrt(N). However, in this case, N would represent the total number of oscillators for both systems A and B combined.

To explain this further, let's say that the number of oscillators for system A is N_A and for system B is N_B. The total number of oscillators for both systems would be N = N_A + N_B. Therefore, the width of the function would be q/sqrt(N_A + N_B).

I hope this helps. If you have any further questions, please don't hesitate to ask. Good luck with your studies!