EBK PHYSICS FOR SCIENTISTS AND ENGINEER
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
6th Edition
ISBN: 9781319321710
Author: Mosca
Publisher: VST
Question
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Chapter 38, Problem 66P

(a)

To determine

Show that the total number of energy states is 23AEF32 .

(a)

Expert Solution
Check Mark

Answer to Problem 66P

It is showed that the total number of energy states is 23AEF32 .

Explanation of Solution

Given:

The density of the electron states in a metal is g(E)=AE12 .

Formula used:

The number of energy states is given by,

  N=0EFg(E)dE

Calculation:

The number of energy states in a metal is calculated as:

  N=0 E Fg(E)dE=0EF(A E 1 2 )dE=2A3[E32]0EF=2AEF323

Conclusion:

Therefore, it is showed that the total number of energy states is 23AEF32 .

(b)

To determine

The fraction of the conduction electrons that are within kT of Fermi energy

(b)

Expert Solution
Check Mark

Answer to Problem 66P

The fraction of the conduction electrons that are within kT of Fermi energy is 32KTEF .

Explanation of Solution

Formula used:

The number of energy states is given by,

  N=0EFg(E)dE

Calculation:

The fraction of number of states that is within kT of the Fermi energy is calculated as:

  kTg( E F )N=kT ( A E F ) 1 2 23AEF 3 2 =32KTEF

Conclusion:

Therefore, the fraction of the conduction electrons that are within kT of the Fermi energy is 32KTEF .

(c)

To determine

The fraction of the conduction electrons of copper that are within kT of Fermi energy at T=300K .

(c)

Expert Solution
Check Mark

Answer to Problem 66P

The fraction of the conduction electrons of copper that are within kT of Fermi energy at T=300K is 5.51×103 .

Explanation of Solution

Formula used:

The expression forthe fraction of the conduction electrons that are within kT of the Fermi energyis given by,

  kTg(EF)N=32KTEF

Calculation:

The value of Fermi energy of copper is EF=7.04eV . The fraction of the conduction electrons of copper that are within kT of Fermi energy at T=300K is calculated as:

  kTg( E F )N=32KTEF=32( 8.62× 10 5 eV/K )×( 300K)( 7.04eV)=5.51×103

Conclusion:

Therefore, the fraction of the conduction electrons of copper that are within kT of Fermi energy at T=300K is 5.51×103 .

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