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Chapter 9: Q9CQ (page 403)

By considering its constituents, determine the dimensions (e.g. length, distance over lime. etc.) of the denominator in equation(9−26). Why is the result sensible?

Short Answer

Expert verified

It follows that the denominator must be dimensionless so that the average energy also has units of energy

Step by step solution

01

Step 1:Equation (26)

Equation (26) writes:

∫N(E)D(E)dE

WhereNis the occupation number or simply the number of particles in a particular energy state,D(E)is the density of states anddEis the energy range.

02

Step 2:

In the above equation,N is dimensionless, D(E)has units of 1 /energy anddE has units of energy. Using dimensional analysis, equation (26) must therefore be dimensionless.

03

denominator must be dimensionless

This result is sensible because equation is one of the recipes to calculate the average energyE¯ Since the equation for average energy has numerator with units of energy, it follows that the denominator must be dimensionless so that the average energy also has units of energy.

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