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Chapter 9: Q59E (page 407)

Density of states (9-39) does not depend on N, the total number of particles in the system; neither does the density of states in equation (9-27). Why not?

Short Answer

Expert verified

The density states do not depend on number of particles in the system.

Step by step solution

01

Formula used

The expression for density of energy state is given by,

D(E)=m32L3π2ℏ32E12

02

Given information from question

The density of state from equation 9.39 is,

D(E)=m32L3π2ℏ32E12

03

 Step 3: Calculate the expression for density 

The expression for density of energy state is calculated as,

D(E)=m32L3π2ℏ32E12=(2s+1)m32Vπ2ℏ32E12      (∵L3=(2s+1)V)

Therefore, the density states do not depend on N,number of particles in the system.

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