Consider the distribution of a total of six energy units to a collection of five

Question

Consider the distribution of a total of six energy units to a collection of five identical but distinguishable particles. (a) How many macro-states are there? (b) Find the microstates, hence the multiplicity for each macrostate state and compare your total microstate to the result that can be obtained using the standard permutation theory. N is the total number of particles, NE is the number of particles with energy E. (c) What is the average number of particles with a particular energy E? (d) What is the probability to measure any particular value of energy of a particle? (e) Plot the probability p(E) as a function of energy and try to find the expression for the Maxwell-Boltzmann probability distribution.

Explanation / Answer

(a) there are 10 macrostates for the distribution of a total of six energy units to a collection of five identical but distinguishable particles.

(b) no of microstates=( N factorial/ n1 factorial ,n2 factorial, n3 factorial....)

here N= total no of particles, n1= no of particle in 1 state

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