- #1

tanaygupta2000

- 208

- 14

- Homework Statement
- Three bosons are to be filled in two energy states with degeneracies 3 and 4 respectively.

(1.) List all the macrostates.

(2.) How many microstates does this 3-particle system has?

(3.) Which macrostate is the most probable one?

- Relevant Equations
- Partition function, Z = ∑g(j)exp(-E(j)/kT)

Upto now I've only dealt with the problems regarding non - degenerate energy states.

Since bosons do not follow Pauli's Exclusion Principle, three bosons can be filled in two energy states (say E

so that there are 2 macrostates (corresponding to levels E

Also the probability of occurrence of

I do not understand the meaning behind the given degeneracies of energy states.

Since bosons do not follow Pauli's Exclusion Principle, three bosons can be filled in two energy states (say E

_{1}and E_{2}) as:E_{1} | E_{2} |

1 boson | 2 bosons |

2 bosons | 1 boson |

3 bosons | 0 bosons |

0 bosons | 3 bosons |

so that there are 2 macrostates (corresponding to levels E

_{1}and E_{2}) and 4 microstates (corresponding to 4 possibilities).Also the probability of occurrence of

- I Possibility = 3!/2! = 3
- II Possibility = 3!/2! = 3
- III Possibility = 3!/3! = 1
- IV Possibility = 3!/0! = 6

I do not understand the meaning behind the given degeneracies of energy states.