Answer to Question #184853 in Quantum Mechanics for Asad

Question

i)                For a system of 3 distinguishable particles distributed in two similar compartments, the total number of microstates corresponding to the condition that no compartment should remain empty are______.

a)     4, b) 6, c) 3, d) 9.

Answer 1

As particles are distinguishable, the possible states depend on the position of each particle, where the position means just in which compartment they are situated. The number of possible states is $2^3=8$, as it is $2 \text{ states of particle A} \times 2 \text{ states of particle B}\times 2 \text{ states of particle C}$. Now we need to exclude the states where one compartiment is empty : there is exactly two such states :

• all particles are in the first compartment
• all particles are in the second compartment

Therefore there is $8-2=6$ microstates where no compartment is empty.

The answer is b.