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Chapter 12: Q22P (page 508)

Consider an object containing 6 one-dimensional oscillators (this object could represent a model of 2 atoms in an Einstein solid). There are 4 quanta of vibrational energy in the object. (a) How many microstates are there, all with the same energy? (b) If you examined a collection of 48,000 objects of this kind, each containing 4 quanta of energy, about how many of these objects would you expect to find in the microstate 000004?

Short Answer

Expert verified

number of microstates = 126

number of objects = 380.95

Step by step solution

01

Given data

Number ofID oscillators (N) = 6

Quanta (n) = 4

02

(a) Determine the number of microstates

The no. of microstates,

Ω=(n+N-1)!n!(N-1)!   =(4+6-1)!4!(6-1)!   =126

03

(b)Determine the number of objects

The no. of objects is given by,

n1=collectionofobjectsΩ =48,000126 =380.95

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