This problem is (17.9) from a book "Thermodynamics and Statistical Mechanics An Integrated Approach by M. Scott Shell" 17.9. In the infinite-state model, particles are independent and each experiences anenergy of €; = en¡, where is a constant and n; > 0 an integer. Find thedistribution of states for a particle, p(n).

For the infinite-state model, the probabilities of microstate at a constant temperature, volume, and number of particles are defined as, ℘n=e-βEnQT,V,NWhere,QT,V,N=∑All microstatese-βEn Where, Q be defined as the partition function.Now given the energy is εi = εni. Therefore, the partition function Q be calculated as, QT,V,N=∑All Microstatese-βEn=∑i=1∞exp-βεni=∑n1......∑nie-βεn1×e-βεn2×........eβεni=∑e-βεniHence the distribution of states be given as, ℘n=e-βEnQT,V,N℘n=e-βεni∑e-βεni

Answered: In the infinite-state model, particles…

In the infinite-state model, particles are independent and each experiences an energy of e; = en, where e is a constant and n; > 0 an integer. Find the distribution of states for a particle, p(n).