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. They are arranged so that one particle occupies each of the three middle energy levels. (This would be state 01110 if the state in which all particles are at the lowest energy level is 30000 and the state in which two particles are at the lowest level and one is at the highest level is 20001.) What is the average energy per particle? Select one: 3.5 J 2.3 J 7.5 J 2.5 J 2 J

Explanation / Answer

Five levels energies are respectively 0.5 J , 1.5 J , 2.5 J , 3.5 J , 4.5 J

For state 01110 the total energy of all particles = 1.5J + 2.5 J + 3.5 J = 7.5 J

For state 30000 , total energy = 3 ( 0.5) = 1.5 J

for state 20001 , total energy = 2( 0.5) + 4.5 = 5.5 J

total enegy of all combinations = 7.5+1.5 + 5.5 = 14.5 J

Average of these three combination gives = 14.5/3 = 4.833 J

Now average energy for 3 particle system = 4.833 J

average nergy per particle = 4.833 / 3 = 1.61 J = 2J     ( rounded value)

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