Problem 6: A system of 6 identical 1-dimensional harmonic oscillators (it could
ID: 1569270 • Letter: P
Question
Problem 6: A system of 6 identical 1-dimensional harmonic oscillators (it could be two atoms of an Einstein model solid). What is the probability that the first oscillator has 2 quanta of vibrational energy when the system has 3 quanta of vibrational energy?
Hint: You may find it useful to consider how many microstates the system has and how many microstates the rest of the system has when the first oscillator has 2 quanta.
A) 5/9 B) 5/18
C) 5/56 D) 5/120
E) 5/216
Explanation / Answer
We have to distribute 3 quanta to 6 oscillator
which can be achieved in:
A=(3+6-1)!/(3!*5!)=56 ways
when 2 quqnta to given to first ocsillator ,1 quanta can be distributed to 5 oscillator in
B=(1+5-1)!/(4!)=5 ways
Hence
probability=B/A=5/56