Chapter 2: Q. 2.7 (page 57)

For an Einstein solid with four oscillators and two units of energy, represent each possible microstate as a series of dots and vertical lines, as used in the text to prove equation $2.9$ .

Short Answer

Expert verified

Possible microstates of dots and vertical lines are $Ω (4, 2) = 10$

Step by step solution

Step :1 Possible microstates

For four oscillators $N = 4$ and two unit of energy $q = 2$ , the possible microstates are:

Step :2 Using the general formula

Using the general formula for the multiplicity of Einstein solid with $N = 4$ and $q = 2$ :

localid="1650337110602" $Ω (N, q) = (\begin{matrix} q + N - 1 \\ q \end{matrix}) = \frac{(q + N - 1)!}{q! (N - 1)!}$

localid="1650337124840" $Ω (4, 2) = (\begin{matrix} 4 + 2 - 1 \\ 2 \end{matrix}) = \frac{(4 + 2 - 1)!}{2! (4 - 1)!} = 10$

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For an Einstein solid with four oscillators and two units of energy, represent each possible microstate as a series of dots and vertical lines, as used in the text to prove equation $2.9$ .

Short Answer

Step by step solution

Step :1 Possible microstates

Step :2 Using the general formula

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For an Einstein solid with four oscillators and two units of energy, represent each possible microstate as a series of dots and vertical lines, as used in the text to prove equation 2.9.

Short Answer

Step by step solution

Step :1 Possible microstates

Step :2 Using the general formula

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Medical Physics

Further Mechanics and Thermal Physics

Physical Quantities And Units

Linear Momentum

Geometrical and Physical Optics

Dynamics

Study anywhere. Anytime. Across all devices.

For an Einstein solid with four oscillators and two units of energy, represent each possible microstate as a series of dots and vertical lines, as used in the text to prove equation $2.9$ .