You are studying a system that has five evenly spaced energy levels. The lowest

Question

You are studying a system that has five evenly spaced energy levels. The lowest energy level (labeled "1") has an energy of 0.5 J. The remaining energy levels (labeled 2-5 in increasing energy) are evenly spaced, with 1 J energy spacing between the levels. There are three particles in the system, and any number of particles can occupy each of the energy levels. If the average energy per particle in the system is 3.5 J, what is the most probable state of the system? (The labeling below shows how many particles are at each energy level. For example, 02010 means 2 particles are at level 2, which has energy 1.5 J, and one particle is at level 4, which has energy 3.5 J.) Select one: 01002

01110

00111

00030

10011

Explanation / Answer

average energy per particle = 3.5 J ,

Hence energy of system = number of particles x average energy per particle = 3 x 3.5 = 10.5 J

Now this energy is possible by system   00030   where all 3 particles are in 4th level whose energy is 3.5 J

Hence total energy = 3 x 3.5 = 10.5 J and average nergy per particle = 10.5/3 = 3.5 J

Another possibility is 00111 , whose total energy becomes = ( 2.5 J + 3.5 J + 4.5 J) = 10.5 J

average nergy per particle = 10.5 J / 3 = 3.5 J

Hence two possibilities present   00030 and 00111

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