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Microstates and multi-dimensional oscillators

  1. Nov 15, 2007 #1
    Consider an object containing 9 one-dimensional oscillators (this object could represent a model of 3 atoms in an Einstein solid). There are 5 quanta of vibrational energy in the object.

    (a) How many microstates are there, all with the same energy?

    1287 microstates

    (b) If you examined a collection of 30000 objects of this kind, each containing 5 quanta of energy, about how many of these objects would you expect to find in the microstate 000000005?


    I got part (a) but I don't know exactly what question 4 is asking? Thanks for the help.
     
  2. jcsd
  3. Apr 17, 2008 #2
    Im trying to work out a similar problem to this one. Does anyone know how to go about solving part B? I'm not sure how one would start the problem. I tried determing the probabilities of 5-0, 0-5, 4-1, 1-4, 3-2, and 2-3, and then used the ration of 0-5 to the sum, but that produced an incorrect answer.
     
  4. Apr 14, 2009 #3
    Re: Microstates...

    I also have a similar problem on WEBASSIGN. My friend got part B, but he never told me HOW, but here is his problem and answer.

    Consider an object containing 9 one-dimensional oscillators (this object could represent a model of 3 atoms in an Einstein solid). There are 5 quanta of vibrational energy in the object.
    How many microstates are there, all with the same energy?
    HIS ANSWER: 1287

    If you examined a collection of 44000 objects of this kind, each containing 5 quanta of energy, about how many of these objects would you expect to find in the microstate 000000005?
    HIS ANSWER: 34.188034
     
  5. Apr 14, 2009 #4
    Re: Microstates...

    I kinda know how he get it
    but with no explaination, so don't ask me
    5/1287= x/44000
    5*44000/1287 = 170.9401
    170.9401/5=34.188034
     
  6. Nov 10, 2011 #5
    Re: Microstates...

    A better way is 44000/1287, that gives the number of objects.
     
  7. Nov 20, 2014 #6
    Here's the reason that works...

    000000005 is just one of the 1287 microstates. Therefore, the number of objects divided by the number of microstates gives you the number of objects that are in any one given microstate.
     
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