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Chapter 10: Q74E (page 470)

Question: The critical temperature lead is 7.2 K. What is the binding energy of its Cooper pairs at zero temperature?

Short Answer

Expert verified

Answer

The binding energy of the Cooper pairs is 217meV.

Step by step solution

01

Given data

The critical temperature of lead is, 7.2 K .

Temperature of cooper pairs is, 0K .

02

Definition of Binding Energy

The superconducting energy gap Eg , the energy needed to split a molecule into its individual atoms, must be equivalent to the energy needed to break a cooper pair.

As per BCS theory, energy at absolute zero shall beEg=3.5kBTc .

Where KB represents Boltzmann's constant andTc represents critical temperature.

03

Determine the Binding Energy

The binding energy of the Cooper pairs is expressed as,

.Eg=3.5kBTc

Substitute 7.2 K→Tc, and 1.38×10-23J/K→kB in the above equation.

Eg=3.5kBTc=3.51.38×10-23 J/K(7.2 K)=3.48×10-22 J1 cV1.6×10-19 J=2.175×10-3 eV1 mcV10-3 eV

Which gives, Eg=2.17 meV.

The binding energy of the Cooper pairs is 2.17 meV.

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